Math3 Derivative and IntegralLaajuus (3 cr)
Code: TZLM3300
Credits
3 op
Teaching language
- Finnish
- English
Responsible person
- Anne Rantakaulio, TKN
- Antti Kosonen, TER, TRY, TRM
- Ida Arhosalo, TSA, TAR
- Harri Varpanen, TIC
- Pekka Varis, TTV
- Kalle Niemi, TLS, TLP
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Enrollment
01.04.2024 - 30.04.2024
Timing
01.05.2024 - 31.07.2024
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Distance learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 15
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Groups
-
UTIVERKKOInstitute of New Industry, online learning (mechanical, logistics and civil engineering)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Tälle toteutukselle ilmoittautuminen on huhtikuussa ja kurssi suoritetaan kesän aikana. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen. Lopppukoeajankohdat ilmoitetaan työtilassa. Konsultointitunteja etäyhteydellä saatetaan kurssin aikana järjestää, mutta niille osallistuminen ei ole välttämätöntä.
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam schedules
Tenttiajankohdat ilmoitetaan myöhemmin työtilassa. Ne sijoittuvat elo- ja syyskuulle.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
04.03.2024 - 30.04.2024
Number of ECTS credits allocated
3 op
Virtual portion
1 op
Mode of delivery
67 % Contact teaching, 33 % Distance learning
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV23S1Tieto- ja viestintätekniikka (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
The course is implemented between 4.3. and 26.4.2024
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam schedules
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Completion alternatives
Online course in Summer 2024
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (75 % correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
04.03.2024 - 30.04.2024
Number of ECTS credits allocated
3 op
Virtual portion
1 op
Mode of delivery
67 % Contact teaching, 33 % Distance learning
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV23S2Tieto- ja viestintätekniikka (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
The course is implemented between 4.3. and 26.4.2024
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam schedules
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Completion alternatives
Online course in Summer 2024
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (75 % correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
04.03.2024 - 30.04.2024
Number of ECTS credits allocated
3 op
Virtual portion
1 op
Mode of delivery
67 % Contact teaching, 33 % Distance learning
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV23S3Tieto- ja viestintätekniikka (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
The course is implemented between 4.3. and 26.4.2024
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam schedules
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Completion alternatives
Online course in Summer 2024
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (75 % correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
04.03.2024 - 30.04.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Ville Arvio
Groups
-
TTV23SMTieto- ja viestintätekniikka (AMK)
-
ZJATTV23SMAvoin amk, Tieto- ja viestintätekniikka, Monimuoto
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
The course is implemented between 4.3. and 26.4.2024
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam schedules
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Completion alternatives
Online course in Summer 2024
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (75 % correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
04.03.2024 - 30.04.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- English
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TIC23S1Bachelor's Degree Programme in Information and Communications Technology
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Two lessons (90min) per week during weeks 10-16.
Materials
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly contact/online lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Employer connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Completion alternatives
Times of the exams will be given in the first lesson of the course.
Further information
Avoin AMK polkuopiskelijat: 5 paikkaa
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
05.02.2024 - 30.04.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 94
Degree programmes
- Bachelor's Degree Programme in Mechanical Engineering
Teachers
- Anne Rantakaulio
Groups
-
TKN23SBKonetekniikka (AMK)
-
ZJATKN23S1Avoin amk, Konetekniikka, Päivä
-
ZJATKN23SMAvoin amk, Konetekniikka, Monimuoto
-
TKN23SMKonetekniikka (AMK)
-
TKN23SAKonetekniikka (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Course is implemented between 5.2. - 30.4.2024.
Materials
Videos in the learning environment, text files, automatic tests, booklet tasks.
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam schedules
Läpäisykoe Examissa viikolta 14 lähtien, arvosanakoe ja monimuotojen läpäisykoe viikolla 17, uusintakoe 1 viikolla 19 ja uusintakoe 2 viikolla 21.
Completion alternatives
Web-based course in Summer 2024
Student workload
Lectures, guided exercises and exam 40 h
Independent work and automatic tests 40 h
Further information
Jatkuva palaute: automaattitestit ja palautettavat tehtävät
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
08.01.2024 - 19.05.2024
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Distance learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 15
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Mechanical Engineering
Teachers
- Ida Arhosalo
Groups
-
UTIVERKKOInstitute of New Industry, online learning (mechanical, logistics and civil engineering)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Tälle toteutukselle ilmoittautuminen on vuodenvaihteessa ja kurssi suoritetaan kevään aikana. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen. Lopppukoeajankohdat ilmoitetaan työtilassa. Konsultointitunteja etäyhteydellä saatetaan kurssin aikana järjestää, mutta niille osallistuminen ei ole välttämätöntä.
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam schedules
Loppukokeita järjestetään loppukeväästä. Ne valvotaan etäyhteydellä. Tarkemmat ajankohdat ilmoitetaan työtilassa kurssin alettua.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
08.01.2024 - 20.05.2024
Number of ECTS credits allocated
3 op
Virtual portion
2 op
Mode of delivery
34 % Contact teaching, 66 % Distance learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Ida Arhosalo
Groups
-
TLS23KMMLogistiikka - tutkinto-ohjelma (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Kevään aikana tapaamisia monimuotoryhmän yhteisen aikataulutuksen mukaisesti. Kokeet loppukeväästä.
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/laskuharjoitukset, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla
Exam schedules
Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
01.01.2024 - 19.05.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- English
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Groups
-
TAR23S1Bachelor's Degree Programme in Automation and Robotics
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Two lessons (90min) per week during weeks 10-15, exam on week 16.
Materials
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly face-to-face lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Employer connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Completion alternatives
Times of the exams will be given in the first lesson of the course.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
20.11.2023 - 04.01.2024
Timing
01.01.2024 - 19.05.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Groups
-
TSA23SR1Sähkö- ja automaatiotekniikka (AMK)
-
TSA23SR2Sähkö- ja automaatiotekniikka (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2023 - 24.08.2023
Timing
16.10.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Groups
-
TSA23KMInsinööri (AMK), sähkö- ja automaatiotekniikka,monimuototeutus
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Syksyn aikana tapaamisia monimuotoryhmän yhteisen aikataulutuksen mukaisesti. Kokeet loppusyksystä.
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/webinaarit, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla.
Exam schedules
Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2023 - 24.08.2023
Timing
28.08.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Distance learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 15
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Mechanical Engineering
Teachers
- Ida Arhosalo
Groups
-
UTIVERKKOInstitute of New Industry, online learning (mechanical, logistics and civil engineering)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Tälle toteutukselle ilmoittautuminen on syksyn alussa ja kurssi suoritetaan syksyn aikana. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen. Lopppukoeajankohdat ilmoitetaan työtilassa. Konsultointitunteja etäyhteydellä saatetaan kurssin aikana järjestää, mutta niille osallistuminen ei ole välttämätöntä.
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam schedules
Loppukokeita järjestetään loppusyksystä. Ne valvotaan etäyhteydellä. Tarkemmat ajankohdat ilmoitetaan työtilassa kurssin alettua.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2023 - 24.08.2023
Timing
28.08.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Virtual portion
2 op
Mode of delivery
34 % Contact teaching, 66 % Distance learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Ida Arhosalo
Groups
-
TLS22SMMLogistiikka - tutkinto-ohjelma (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Syksyn aikana tapaamisia monimuotoryhmän yhteisen aikataulutuksen mukaisesti. Kokeet loppusyksystä.
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/webinaarit, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla.
Exam schedules
Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2023 - 24.08.2023
Timing
28.08.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 55
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Peppi Teacher
- Peppi Ohjaaja
- Kalle Niemi
Scheduling groups
- TLS22SA (Size: 30. Open UAS: 0.)
- TLS22SB (Size: 30. Open UAS: 0.)
Groups
-
TLS22S1Logistiikka - tutkinto-ohjelma (AMK)
Small groups
- TLS22SA
- TLS22SB
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Course is implemented between 30.10. - 17.12.2023.
Materials
Videos in the learning environment, text files, automatic tests, booklet tasks.
Extra material in Applied Calculus (http://www.opentextbookstore.com/details.php?id=14)
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam schedules
Final exam in week 45, resit 1 in week 47 and resit 2 in week 2/2024.
Completion alternatives
Web-based course in Spring and Summer 2024
Student workload
Lectures, guided exercises and exam 30 h
Independent work and automatic tests 51 h
Further information
Continuous feedback: automated tests and returnable tasks
Final exam
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2023 - 24.08.2023
Timing
28.08.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- English
Seats
0 - 30
Degree programmes
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Kalle Niemi
Groups
-
TLP22S1Bachelor's Degree Programme in Purchasing and Logistics Engineering
-
TLP23VSBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Course is implemented between 30.10. - 17.12.2023.
Materials
Videos in the learning environment, text files, automatic tests, booklet tasks.
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam schedules
Läpäisykoe Examissa viikolta 48 lähtien, arvosanakoe viikolla 17, uusintakoe 1 viikolla 19 ja uusintakoe 2 viikolla 21.
Student workload
Lectures, guided exercises and exam 30 h
Independent work and automatic tests 51 h
Further information
Jatkuva palaute: automaattitestit ja palautettavat tehtävät
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.04.2023 - 30.04.2023
Timing
01.05.2023 - 31.08.2023
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Distance learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 40
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
LOGRAKVERKKOLogistiikan ja rakentamisen verkko-opetus
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Tälle toteutukselle ilmoittautuminen on huhtikuussa ja kurssi suoritetaan kesän aikana. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen. Lopppukoeajankohdat ilmoitetaan työtilassa. Konsultointitunteja etäyhteydellä saatetaan kurssin aikana järjestää, mutta niille osallistuminen ei ole välttämätöntä.
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam schedules
Tenttiajankohdat ilmoitetaan myöhemmin työtilassa. Ne sijoittuvat viikoille 32-35.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Distance learning
Unit
School of Technology
Teaching languages
- Finnish
Seats
0 - 70
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Ville Arvio
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
The course is implemented between 6.3.2023 and 21.4.2023.
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam schedules
The course timetable is agreed on at the beginning of the course and then published in the e-learning environment.
Completion alternatives
Online course in Summer 2023
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (80% correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Distance learning
Unit
School of Technology
Teaching languages
- Finnish
Seats
0 - 70
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Ville Arvio
Groups
-
ZJATTV22SMAvoin amk, Tieto- ja viestintätekniikka, Monimuoto
-
TTV22SMTieto- ja viestintätekniikka (AMK)
-
TTV22SM2Tieto- ja viestintätekniikka (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
The course is implemented between 6.3.2023 and 28.4.2023.
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam schedules
The course timetable is agreed on at the beginning of the course and then published in the e-learning environment.
Completion alternatives
Online course in Summer 2023
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (80% correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Pekka Varis
Groups
-
TTV22S1Tieto- ja viestintätekniikka (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Kevätlukukauden 2023 toinen puolisko.
Materials
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 2 -oppikirjaa.
Teaching methods
Kontaktiopetus 2+2 h/viikko (luentoja ja laskuharjoituksia)
Videoluentoja
Itsenäisiä laskuharjoituksia
Exam schedules
Tentin ajankohdat ja uusintapäivät julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.
Completion alternatives
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
Kontaktiopetus noin 25 h. Joillakin viikoilla voi olla etäopetusta Dynamon tilojen käytettävyydestä riippuen.
Harjoitukset kontaktituntien ulkopuolella noin 25 h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 25 h
Further information
Arviointimenetelmä:
Kurssin lopussa pidetään koe. Viikoittaisista kotitehtävistä saa kokeeseen lisäpisteitä.
Suositellaan valitsemaan myös opintojakso Mat3 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- English
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TIC22S1Bachelor's Degree Programme in Information and Communications Technology
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Two lessons (90min) per week during weeks 10-16.
Materials
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly contact/online lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Employer connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Completion alternatives
Times of the exams will be given in the first lesson of the course.
Further information
Avoin AMK polkuopiskelijat: 5 paikkaa
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 30
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Pekka Varis
Groups
-
ZJATTV22S2Avoin amk, Tieto- ja viestintätekniikka, Päivä
-
TTV22S2Tieto- ja viestintätekniikka (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Kevätlukukauden 2023 toinen puolisko.
Materials
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 2 -oppikirjaa.
Teaching methods
Kontaktiopetus 2+2 h/viikko (luentoja ja laskuharjoituksia)
Videoluentoja
Itsenäisiä laskuharjoituksia
Exam schedules
Tentin ajankohdat ja uusintapäivät julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.
Completion alternatives
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
Kontaktiopetus noin 25 h. Joillakin viikoilla voi olla etäopetusta Dynamon tilojen käytettävyydestä riippuen.
Harjoitukset kontaktituntien ulkopuolella noin 25 h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 25 h
Further information
Arviointimenetelmä:
Kurssin lopussa pidetään koe. Viikoittaisista kotitehtävistä saa kokeeseen lisäpisteitä.
Suositellaan valitsemaan myös opintojakso Mat3 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV22S3Tieto- ja viestintätekniikka (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
The course is implemented between 6.3. and 21.4.2023
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam schedules
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Completion alternatives
Online course in Summer 2023
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (80% correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 30
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Ville Arvio
Groups
-
TTV22S5Tieto- ja viestintätekniikka (AMK)
-
ZJATTV22S5Avoin amk, Tieto- ja viestintätekniikka, Päivä
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
The course is implemented between 6.3.2023 and 28.4.2023.
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam schedules
The course timetable is agreed on at the beginning of the course and then published in the e-learning environment.
Completion alternatives
Online course in Summer 2023
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (80% correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV22S4Tieto- ja viestintätekniikka (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
The course is implemented between 6.3. and 21.4.2023
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Lehtola, Rantakaulio - Tekninen matematiikka 2 (in Finnish)
Teaching methods
Lectures, guided exercises, independent work
Exam schedules
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Completion alternatives
Online course in Summer 2023
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Further information
The course includes home assignments, intermediate tests, a pass examination and a grade examination. It is possible to pass the course with grade 1 by taking the pass examination (80% correct) based on fundamentals studied in the course. A higher grade requires participation in the grade examination. To be able to participate in the pass examination and grade examination, the compulsory parts (home assignments and intermediate tests) must be completed acceptably.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Pekka Varis
- Ville Sivil
Groups
-
TSA22SR2Sähkö- ja automaatiotekniikka (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
06.03.2023 - 28.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 60
Degree programmes
- Bachelor's Degree Programme in Electrical and Automation Engineering
Teachers
- Sirpa Alestalo
- Ville Sivil
Teacher in charge
Ida Arhosalo
Groups
-
ZJATSA22S1Avoin amk, Sähkö- ja automaatiotekniikka, Päivä
-
TSA22SR1Sähkö- ja automaatiotekniikka (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
luennot/laskuharjoitukset 2*2/vko viikoilla 10-16
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/laskuharjoitukset, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla
Exam schedules
Loppukoe viikolla 16. Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Completion alternatives
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Kurssista löytyy myös itsenäisesti tehtävä verkkototeutus. Jos kontaktiopetukseen ei halua osallistua, kannattaa ilmoittautua verkkototeutukselle.
Student workload
Yhteensä 81h
Luennot/laskuharjoitukset/tentti 25-30h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 50-60h
Further information
Opintojaksoon liittyy kotitehtäviä, välitestejä, läpäisytesti ja arvosanakoe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (80 % oikein) perusasioihin liittyvän läpäisytestin. Korkeampi arvosana edellytttää arvosanakokeeseen osallistumista. Jotta läpäisytestiin ja arvosanakokeeseen voi osallistua, täytyy opintojakson pakolliset suoritteet (kotitehtävät ja välitestit) olla hyväksytysti tehty.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
21.11.2022 - 05.01.2023
Timing
06.03.2023 - 30.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- English
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
TAR22S1Bachelor's Degree Programme in Automation and Robotics
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Two lessons (90min) per week during weeks 10-15, exam on week 16.
Materials
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly contact/online lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Employer connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Completion alternatives
Times of the exams will be given in the first lesson of the course.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 05.01.2023
Timing
09.01.2023 - 26.02.2023
Number of ECTS credits allocated
3 op
Virtual portion
2 op
Mode of delivery
34 % Contact teaching, 66 % Distance learning
Unit
School of Technology
Teaching languages
- Finnish
Seats
0 - 60
Degree programmes
- Bachelor's Degree Programme in Energy and Environmental Technology
Teachers
- Antti Kosonen
Groups
-
TER22S1Energia- ja ympäristötekniikka (AMK)
-
TER22SMEnergia- ja ympäristötekniikka (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
This course is implemented 23.1.2023 - 2.4.2023 instead of the previously announced 9.1.2023 - 26.2.2023.
Lectures will be streamed online.
Guided exercises will be held at campus or online depending on the implementation of your degree programme.
Materials
Written material, video material and exercises prepared by teacher.
Appropriate textbooks in Finnish:
- Alestalo, S., Lehtola, P., Nieminen, T. & Rantakaulio, A. 2011. Tekninen matematiikka 1. 1. uusittu painos. Tampere: Tammertekniikka.
- Henttonen, J., Peltomäki, J. & Uusitalo, S. 2003. Tekniikan matematiikka: 1. Helsinki: Edita.
Teaching methods
Lectures, guided exercises, independent work, exams
Exam schedules
Exam to pass the course will be done independently during the course in e-exam studio or as a more traditional supervised exam during week 8, depending on the implementation of your degree programme.
The grade-determining exam will take place during week 8.
First resit 22.3.2023
Second resit 12.4.2023
Completion alternatives
Face-to-face and online implementations are available in spring and in autumn. It is also possible to attend the course online during summer 2023.
Student workload
For six weeks:
Lectures 2 * 45 min
Exercises (depending on programme): 3 * 45 min or 2 * 45 min
Additionally:
Exams approximately 4 h
Independent work approximately 55 - 60 h
Content scheduling
Themes will be discussed in the following order (one week / theme):
1. Definition of the Derivative
2. Symbolic Differentiation
3. Applications of the Derivative
4. Definition of the Integral and Symbolic Integration
5. The Fundamental Theorem of Calculus
6. Applications of Integration
Further information
Assessment is based on two-part final exam and exercises.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 19.05.2023
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Distance learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 5
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
LOGRAKVERKKOLogistiikan ja rakentamisen verkko-opetus
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Tälle toteutukselle ilmoittautuminen on vuodenvaihteessa ja kurssi suoritetaan kevään aikana. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen. Lopppukoeajankohdat ilmoitetaan työtilassa. Konsultointitunteja etäyhteydellä saatetaan kurssin aikana järjestää, mutta niille osallistuminen ei ole välttämätöntä.
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam schedules
Loppukokeita järjestetään viikoilla 8-17. Ne valvotaan etäyhteydellä. Tarkemmat ajankohdat ilmoitetaan työtilassa kurssin alettua.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 30.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 55
Degree programmes
- Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
- Anne Rantakaulio
Teacher in charge
Anne Rantakaulio
Scheduling groups
- TRY22SA (Size: 35. Open UAS: 0.)
- TRY22SB (Size: 35. Open UAS: 0.)
Groups
-
ZJATRY22S1Avoin amk, Rakennus- ja yhdyskuntatekniikka, Päivä
-
TRY22S1Rakennus- ja yhdyskuntatekniikka (AMK)
Small groups
- TRY22SA
- TRY22SB
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Course is implemented between 20.2. - 28.4.2023.
Materials
Videos in the learning environment, text files, automatic tests, booklet tasks.
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam schedules
Läpäisy- ja arvosanakoe viikolla 17, uusintakoe 1 viikolla 19 ja uusintakoe 2 viikolla 21.
Completion alternatives
Web-based course in Summer 2023
Student workload
Lectures, guided exercises and exam 40 h
Independent work and automatic tests 40 h
Further information
Jatkuva palaute: automaattitestit ja palautettavat tehtävät
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 21.05.2023
Number of ECTS credits allocated
3 op
Virtual portion
1 op
Mode of delivery
67 % Contact teaching, 33 % Distance learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 40
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
TLS22KMMLogistiikan tutkinto-ohjelma (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Kevään aikana tapaamisia monimuotoryhmän yhteisen aikataulutuksen mukaisesti. Kokeet loppukeväästä.
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/laskuharjoitukset, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla
Exam schedules
Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2022 - 05.01.2023
Timing
01.01.2023 - 21.05.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 100
Degree programmes
- Bachelor's Degree Programme in Mechanical Engineering
Teachers
- Anne Rantakaulio
Teacher in charge
Anne Rantakaulio
Groups
-
TKN22SAKonetekniikka (AMK)
-
TKN22SBKonetekniikka (AMK)
-
ZJATKN22SMAvoin amk, Konetekniikka, Monimuoto
-
TKN22S1Konetekniikka (AMK)
-
TKN22SMKonetekniikka (AMK)
-
ZJATKN22S1Avoin amk, Konetekniikka, Päivä
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Course is implemented between 20.2. - 28.4.2022.
Materials
Videos in the learning environment, text files, automatic tests, booklet tasks.
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam schedules
Läpäisy- ja arvosanakoe viikolla 17, sen uusintakoe 1 viikolla 19 ja uusintakoe 2 viikolla 21.
Completion alternatives
Web-based course in Summer 2023
Student workload
Lectures, guided exercises and exam 40 h
Independent work and automatic tests 40 h
Further information
Jatkuva palaute: automaattitestit ja palautettavat tehtävät
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2022 - 25.08.2022
Timing
05.09.2022 - 18.11.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 30
Degree programmes
- Bachelor's Degree Programme in Electrical and Automation Engineering
Teachers
- Anne Rantakaulio
Teacher in charge
Pasi Lehtola
Groups
-
TSA22KMInsinööri (AMK), sähkö- ja automaatiotekniikka,monimuototeutus
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Course is implemented between 5.9. - 18.11.2022.
Materials
Videos in the learning environment, text files, automatic tests, assignments, booklet tasks.
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, assignments, exam.
Exam schedules
Läpäisy- ja arvosanakoe viikolla 46. Uusintakoe 1 viikolla 49 ja uusintakoe 2 viikolla 2.
Completion alternatives
Web-based course in Summer 2023
Student workload
Lectures, guided exercises and exam 28 h
Independent work 53 h
Further information
Jatkuva palaute: automaattitestit ja palautettavat tehtävät
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2022 - 25.08.2022
Timing
29.08.2022 - 14.10.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Teaching languages
- Finnish
Seats
0 - 55
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Scheduling groups
- TLS21SA (Size: 35. Open UAS: 0.)
- TLS21SB (Size: 35. Open UAS: 0.)
Groups
-
TLS21S1Logistiikan tutkinto-ohjelma (AMK)
Small groups
- TLS21SA
- TLS21SB
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
luennot/laskuharjoitukset 2*2/vko viikoilla 35-41
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/laskuharjoitukset, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla
Exam schedules
Loppukoe kurssin viimeisellä luentokerralla (vko 41). Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Completion alternatives
Kurssista löytyy myös itsenäisesti tehtävä verkkototeutus. Jos kontaktiopetukseen ei halua osallistua, kannattaa ilmoittautua verkkototeutukselle.
Student workload
Yhteensä 81h
Luennot/laskuharjoitukset/tentti 25-30h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 50-60h
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2022 - 25.08.2022
Timing
29.08.2022 - 21.12.2022
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Distance learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 5
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
LOGRAKVERKKOLogistiikan ja rakentamisen verkko-opetus
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Tälle toteutukselle ilmoittautuminen on elokuussa. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen. Voit osallistua viikolla 41 loppukokeeseen Rajakadulla, muut loppukokeet myöhemmin syksyllä valvotaan etäyhteydellä. Lopppukoeajankohdat ilmoitetaan työtilassa. Konsultointitunteja etäyhteydellä saatetaan kurssin aikana järjestää, mutta niille osallistuminen ei ole välttämätöntä.
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam schedules
Loppukokeita järjestetään viikoilla 41-49. Viikon 41 kokeet on Rajakadulla luokassa. Viikoilla 43-49 järjestetään 3 etävalvottua koetta.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.08.2022 - 25.08.2022
Timing
29.08.2022 - 31.10.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- English
Seats
0 - 30
Degree programmes
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
TLP22VSBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
-
TLP21S1Bachelor's Degree Programme in Purchasing and Logistics Engineering
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Two lessons (90min) per week during weeks 35-40, exam on week 41.
Materials
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly face-to-face lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Employer connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Completion alternatives
Times of the exams will be given in the first lesson of the course.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
07.03.2022 - 29.04.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Pekka Varis
Groups
-
TTV21S1Tieto- ja viestintätekniikka (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Kevätlukukauden 2022 toinen puolisko.
Materials
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 2 -oppikirjaa.
Teaching methods
Kontaktiopetus 2+2 h/viikko (luentoja ja laskuharjoituksia)
Videoluentoja
Itsenäisiä laskuharjoituksia
Exam schedules
Tentin ajankohdat ja uusintapäivät julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.
Completion alternatives
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
Kontaktiopetus noin 25 h. Joillakin viikoilla voi olla etäopetusta Dynamon tilojen käytettävyydestä riippuen.
Harjoitukset kontaktituntien ulkopuolella noin 25 h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 25 h
Further information
Arviointimenetelmä:
Kurssin lopussa pidetään koe. Viikoittaisista kotitehtävistä saa kokeeseen lisäpisteitä.
Suositellaan valitsemaan myös opintojakso Mat1 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
07.03.2022 - 29.04.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Pekka Varis
Groups
-
ZJA21STIPPTVAvoin amk, tekniikka, Tieto-ja viestintätekniikka, päivä
-
TTV21S2Tieto- ja viestintätekniikka (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Kevätlukukauden 2022 toinen puolisko.
Materials
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 2 -oppikirjaa.
Teaching methods
Kontaktiopetus 2+2 h/viikko (luentoja ja laskuharjoituksia)
Videoluentoja
Itsenäisiä laskuharjoituksia
Exam schedules
Tentin ajankohdat ja uusintapäivät julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.
Completion alternatives
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
Kontaktiopetus noin 25 h. Joillakin viikoilla voi olla etäopetusta Dynamon tilojen käytettävyydestä riippuen.
Harjoitukset kontaktituntien ulkopuolella noin 25 h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 25 h
Further information
Arviointimenetelmä:
Kurssin lopussa pidetään koe. Viikoittaisista kotitehtävistä saa kokeeseen lisäpisteitä.
Suositellaan valitsemaan myös opintojakso Mat1 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
07.03.2022 - 29.04.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV21S3Tieto- ja viestintätekniikka (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Opintojakso toteutetaan viikoilla 11 - 17 (14.3. - 29.4.2022) Lutakon kampuksella kontaktina Dynamolla tai etänä Zoomissa
Materials
Opintojakson pääasiallisena materiaalina toimivat opettajan jakama kirjallinen materiaali sekä videomateriaali verkko-oppimisympäristössä.
Opintojaksoon liittyvä suositeltava kirjallisuus:
- Lehtola, Rantakaulio - Tekninen matematiikka 2
Teaching methods
Kontaktiopetus 3+2 h /viikko, ohjatut laskuharjoitukset, itsenäinen työskentely
Exam schedules
Opintojakson tarkempi aikataulu sovitaan opintojakson aloitustapaamisessa ja julkaistaan verkko-oppimisympäristössä.
Completion alternatives
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
Opintojakson laskennallinen kuormitus on 3op * 27h/op = 81h.
Kontaktiopetus noin 35h
Harjoitukset kontaktituntien ulkopuolella noin 25h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 20h
Further information
Opintojaksoon liittyy kotitehtäviä, välitestejä, läpäisytesti ja koe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (75 % oikein) perusasioihin liittyvä läpäisytesti. Korkeampi arvosana edellytttää kokeeseen osallistumista. Jotta läpäisytestiin ja kokeeseen voi osallistua, täytyy opintojakson kotitehtävät ja välitestit olla suoritettuna hyväksytysti.
Avoin AMK 10 paikkaa
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
07.03.2022 - 29.04.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
Groups
-
TTV21S5Tieto- ja viestintätekniikka (AMK)
-
ZJA21STIPPTVAvoin amk, tekniikka, Tieto-ja viestintätekniikka, päivä
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Opintojakso toteutetaan viikoilla 11 - 17 (14.3. - 29.4.2022) Lutakon kampuksella kontaktina Dynamolla tai etänä Zoomissa
Materials
Opintojakson pääasiallisena materiaalina toimivat opettajan jakama kirjallinen materiaali sekä videomateriaali verkko-oppimisympäristössä.
Opintojaksoon liittyvä suositeltava kirjallisuus:
- Lehtola, Rantakaulio - Tekninen matematiikka 2
Teaching methods
Kontaktiopetus 3+2 h /viikko, ohjatut laskuharjoitukset, itsenäinen työskentely
Exam schedules
Opintojakson tarkempi aikataulu sovitaan opintojakson aloitustapaamisessa ja julkaistaan verkko-oppimisympäristössä.
Completion alternatives
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
Opintojakson laskennallinen kuormitus on 3op * 27h/op = 81h.
Kontaktiopetus noin 35h
Harjoitukset kontaktituntien ulkopuolella noin 25h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 20h
Further information
Opintojaksoon liittyy kotitehtäviä, välitestejä, läpäisytesti ja koe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (75 % oikein) perusasioihin liittyvä läpäisytesti. Korkeampi arvosana edellytttää kokeeseen osallistumista. Jotta läpäisytestiin ja kokeeseen voi osallistua, täytyy opintojakson kotitehtävät ja välitestit olla suoritettuna hyväksytysti.
Avoin AMK 10 paikkaa
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
07.03.2022 - 29.04.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 110
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Kalle Niemi
Groups
-
TTV21SMTieto- ja viestintätekniikka (AMK)
-
ZJA21STPMTVAvoin amk, tekniikka, Tieto- ja viestintätekniikka, verkko
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Opintojakso toteutetaan 7.3.2022 - 30.4.2022.
Materials
Luentomoniste ja harjoitustehtävät Moodlessa.
Teaching methods
Verkkoluennot ja -ohjaus, itsenäinen työskentely ja verkkotyöskentely.
Employer connections
Kurssin sisältö pyritään kytkemään työelämässä esiintyviin ongelmiin.
Exam schedules
Kurssin tenttikäytänteet ilmoitetaan kurssin ensimmäisellä tapaamiskerralla.
Completion alternatives
Hyväksilukemisen menettelytavat kuvataan tutkintosäännössä ja opinto-oppaassa. Opintojakson opettaja antaa lisätietoa mahdollisista opintojakson erityiskäytänteistä.
Student workload
Itsenäistä opiskelua 81 h
Further information
Opintojakso arvioidaan kokeen tai kokeiden ja laskuharjoituksista kerättävien pisteiden perusteella.
Avoin AMK verkko-opinnot 20 paikkaa
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
07.03.2022 - 29.04.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- English
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
ZJA21STPICAvoin amk, tekniikka, Information and Communications Technology, päivä
-
TIC21S1Bachelor's Degree Programme in Information and Communications Technology
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Two lessons (90min) per week during weeks 10-16.
Materials
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly contact/online lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Employer connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Completion alternatives
Times of the exams will be given in the first lesson of the course.
Further information
Avoin AMK polkuopiskelijat: 5 paikkaa
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
07.03.2022 - 22.04.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 60
Degree programmes
- Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
- Anne Rantakaulio
Teacher in charge
Anne Rantakaulio
Scheduling groups
- TRY21SA (Size: 30. Open UAS: 0.)
- TRY21SB (Size: 30. Open UAS: 0.)
Groups
-
TRY21S1Rakennus- ja yhdyskuntatekniikka (AMK)
-
ZJA21STPPRYAvoin amk, tekniikka, Rakennus- ja yhdyskuntatekniikka, päivä
Small groups
- TRY21SA
- TRY21SB
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Course is implemented between 7.3. - 22.4.2022.
Materials
Videos in the learning environment, text files, automatic tests, booklet tasks.
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam schedules
Schedule will be agreed on the first contact lesson of the course.
Completion alternatives
Web-based course in Summer 2022
Student workload
Lectures, guided exercises and exam 40 h
Independent work and automatic tests 40 h
Further information
Avoin AMK 5
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.03.2022 - 31.05.2022
Timing
01.03.2022 - 31.08.2022
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Distance learning
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 10
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
LOGAKTIIVILogistiikan aktiivitoteutukset
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin loppukoetta.
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam schedules
Elokuussa loppukoe ja kaksi uusintaa, tarkemmat tenttiajankohdat ilmoitetaan myöhemmin.
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Further information
Avoin AMK 10
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 18.03.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 45
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
TLS21KMMLogistiikan tutkinto-ohjelma (AMK)
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen.
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Kontaktitunteja ja/tai konsultaatiota etäyhteydellä pidettävissä webinaareissa. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam schedules
Tenttiajankohdat ilmoitetaan myöhemmin työtilassa.
Student workload
konsultaatiotunnit + itsenäinen työskentely (teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Further information
Avoin AMK 10
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 20.05.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 80
Degree programmes
- Bachelor's Degree Programme in Mechanical Engineering
Teachers
- Anne Rantakaulio
Teacher in charge
Anne Rantakaulio
Scheduling groups
- TKN21S1, päivätoteutus (Size: 50. Open UAS: 0.)
- TKN21SM, monimuotototeutus (Size: 30. Open UAS: 0.)
Groups
-
ZJA21STPMKOAvoin amk, tekniikkan Konetekniikka, monimuoto
-
ZJA21STPPKOAvoin amk, tekniikka, Konetekniikka, päivä
-
TKN21S1Konetekniikka
-
TKN21SMKonetekniikka
Small groups
- TKN21S1,
- TKN21SM
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Course is implemented between 10.1. - 25.3.2022.
Materials
Videos in the learning environment, text files, automatic tests, booklet tasks.
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam schedules
Schedule will be agreed on the first contact lesson of the course.
Completion alternatives
Web-based course in Summer 2022
Student workload
Lectures, guided exercises and exam 40 h
Independent work and automatic tests 40 h
Further information
Avoin AMK 5
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 20.05.2022
Number of ECTS credits allocated
3 op
Virtual portion
1 op
Mode of delivery
67 % Contact teaching, 33 % Distance learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 70
Degree programmes
- Bachelor's Degree Programme in Energy and Environmental Technology
Teachers
- Antti Kosonen
Teacher in charge
Antti Kosonen
Scheduling groups
- Päiväryhmä (Size: 40. Open UAS: 0.)
- Monimuoto (Size: 40. Open UAS: 0.)
Groups
-
ZJA21STPPENAvoin amk, tekniikka Enegia- ja ympäristötekniikka, päivä
-
ZJA21STPMENAvoin amk, tekniikka, Energia- ja ympäristöteniikka, monimuoto
-
TER21S1Energia- ja ympäristötekniikka (AMK)
-
TER21SMEnergia- ja ympäristötekniikka (AMK)
Small groups
- Päiväryhmä
- Monimuoto
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Opintojakso toteutetaan 10.1.2022 - 27.2.2022
Luennot toteutetaan lähiopetuksena sekä live-streamina verkossa.
Laskuharjoitukset lähiopetuksena päivätoteutuksen opiskelijoille ja verkossa monimuotototeutuksen opiskelijoille.
Teaching methods
Opintojakso koostuu luennoista, ohjatuista laskuharjoituksista, itsenäisestä harjoittelusta ja kokeista.
Exam schedules
Ilmoitetaan opintojakson alussa.
Student workload
3op * 27h/op = 81h
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 20.05.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 60
Degree programmes
- Bachelor's Degree Programme in Electrical and Automation Engineering
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
TSA21SASähkö- ja automaatiotekniikka (AMK)
-
ZJA21STPPSAAvoin amk, tekniikka, Sähkö ja automaatiotekniikka, päivä
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
luennot/laskuharjoitukset 2*2/vko viikoilla 2-8
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/laskuharjoitukset, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla
Exam schedules
Loppukoe kurssin viimeisellä luentokerralla (vko 8). Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Luennot/laskuharjoitukset/tentti 25-30h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 50-60h
Further information
Avoin AMK 5 paikkaa
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.11.2021 - 09.01.2022
Timing
01.01.2022 - 15.05.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
- Bachelor's Degree Programme in Information and Communications Technology
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Groups
-
TSA21SBSähkö- ja automaatiotekniikka (AMK)
-
ZJA21STPPSAAvoin amk, tekniikka, Sähkö ja automaatiotekniikka, päivä
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
luennot/laskuharjoitukset 2*2/vko viikoilla 2-8
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Luennot/laskuharjoitukset, itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla
Exam schedules
Loppukoe kurssin viimeisellä luentokerralla (vko 8). Tarkempi ajankohta ja uusinta-ajankohdat täsmennetään ensimmäisellä luentokerralla.
Student workload
Yhteensä 81h
Luennot/laskuharjoitukset/tentti 25-30h
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) 50-60h
Further information
Avoin AMK 5 paikkaa
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.
Enrollment
01.10.2021 - 28.02.2022
Timing
01.10.2021 - 31.05.2022
Number of ECTS credits allocated
3 op
Virtual portion
3 op
Mode of delivery
Distance learning
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 5
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
- Bachelor's Degree Programme in Energy and Environmental Technology
- Bachelor's Degree Programme in Electrical and Automation Engineering
- Bachelor's Degree Programme in Mechanical Engineering
Teachers
- Ida Arhosalo
Teacher in charge
Ida Arhosalo
Groups
-
ZJA21STAvoin AMK, tekniikka
-
LOGAKTIIVILogistiikan aktiivitoteutukset
-
ZJA22KTAvoin AMK, tekniikka
Objective
The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.
Content
The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.
Location and time
Tälle toteutukselle ilmoittautuminen alkaa lokakuun alussa ja päättyy helmikuun loppuun mennessä. Lähetä ilmoittautuessasi myös sähköposti osoitteeseen ida.arhosalo@jamk.fi, jotta sinut huomataan heti hyväksyä toteutukselle! Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista. Harjoituksissa on vapaa etenemistahti, mutta harjoitukset on oltava tehtynä ennen kuin voi ilmoittautua loppukokeeseen. Loppukokeita järjestetään vähintään kerran kuussa maaliskuusta alkaen (ajankohdat ilmoitetaan työtilassa). Konsultointitunteja etäyhteydellä järjestetään tarpeen mukaan. Niille osallistuminen ei ole välttämätöntä ja ajankohdat ilmoitetaan myöhemmin työtilassa.
Materials
Oppimateriaali löytyy Moodlesta. Tukimateriaalina voi käyttää esimerkiksi Lehtola, Rantakaulio: Tekninen matematiikka 2 -kirjaa.
Teaching methods
Itsenäinen opiskelu Moodlesta löytyvän kirjallisen materiaalin sekä videomateriaalin avulla. Tarvittaessa konsultaatiota etäyhteydellä pisettävissä webinaareissa. Työtilassa on harjoituksia, jotka pitää tehdä ennen loppukokoeeseen ilmoittautumista.
Exam schedules
Tenttiajankohdat ilmoitetaan myöhemmin työtilassa. Lähetä ilmoittautuessasi myös sähköposti osoitteeseen ida.arhosalo@jamk.fi, jotta sinut huomataan heti hyväksyä toteutukselle!
Student workload
Itsenäinen työskentely (Teoriamateriaalin opiskelu ja harjoitusten laskeminen) + tentti 81h
Further information
Avoin AMK 10
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.
Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.
Assessment criteria, good (3)
Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly
Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.
Assessment criteria, excellent (5)
You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.
Qualifications
You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.