Math2 FunctionsLaajuus (3 cr)
Code: TZLM2300
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023 - 04.01.2024
Timing
08.01.2024 - 23.02.2024
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented between 8.1. and 23.2.24.
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Alestalo, Lehtola, Nieminen, Rantakaulio - Tekninen matematiikka 1 (in Finnish)
- Henttonen, Peltomäki, Uusitalo - Tekniikan matematiikka 1 (in Finnish)
- 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.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023 - 04.01.2024
Timing
08.01.2024 - 23.02.2024
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Two lessons (90min) per week during weeks 2-8.
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.
Exam schedules
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023 - 04.01.2024
Timing
08.01.2024 - 23.02.2024
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented between 8.1. and 23.2.24
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Alestalo, Lehtola, Nieminen, Rantakaulio - Tekninen matematiikka 1 (in Finnish)
- Henttonen, Peltomäki, Uusitalo - Tekniikan matematiikka 1 (in Finnish)
- 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.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023 - 04.01.2024
Timing
08.01.2024 - 23.02.2024
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented between 8.1. and 23.2.24
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Alestalo, Lehtola, Nieminen, Rantakaulio - Tekninen matematiikka 1 (in Finnish)
- Henttonen, Peltomäki, Uusitalo - Tekniikan matematiikka 1 (in Finnish)
- 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.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023 - 04.01.2024
Timing
08.01.2024 - 23.02.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
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
- Ville Arvio
Groups
-
TTV23SMTieto- ja viestintätekniikka (AMK)
-
ZJATTV23SMAvoin amk, Tieto- ja viestintätekniikka, Monimuoto
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented between 8.1. and 23.2.24
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Alestalo, Lehtola, Nieminen, Rantakaulio - Tekninen matematiikka 1 (in Finnish)
- Henttonen, Peltomäki, Uusitalo - Tekniikan matematiikka 1 (in Finnish)
- 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.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
20.11.2023 - 04.01.2024
Timing
08.01.2024 - 19.05.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 60
Degree programmes
- Bachelor's Degree Programme in Electrical and Automation Engineering
Teachers
- Pekka Varis
Groups
-
TSA23SR1Sähkö- ja automaatiotekniikka (AMK)
-
TSA23SR2Sähkö- ja automaatiotekniikka (AMK)
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Kevätlukukauden 2024 ensimmäinen puolisko.
Materials
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 -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 Mat2 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
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 Construction Management
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Ida Arhosalo
Groups
-
TAR23S1Bachelor's Degree Programme in Automation and Robotics
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Two lessons(90min) per week during weeks 2-8.
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.
Exam schedules
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 20h independent studying of theory
approx. 30h independent studying of exercises
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
23.08.2023 - 01.11.2024
Timing
20.11.2023 - 09.02.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 55
Degree programmes
- Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
- Antti Kosonen
Scheduling groups
- TRY23SA (Size: 30. Open UAS: 0.)
- TRY23SB (Size: 30. Open UAS: 0.)
Groups
-
TRY23S1Rakennus- ja yhdyskuntatekniikka (AMK)
-
ZJATRY23S1Avoin amk, Rakennus- ja yhdyskuntatekniikka, Päivä
Small groups
- TRY23SA
- TRY23SB
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Course is implemented between 20.11.2023.-11.2.2024
Materials
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo - Lehtola - Nieminen - Rantakaulio: Tekninen matematiikka 1 and in Lehtola - Rantakaulio: Tekninen matematiikka 2
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam schedules
Test to pass the course in Exam studio January 14 to March 7.
Grading exam in week 6, 1st resit in week 10 and 2nd resit on week 12.
Completion alternatives
Web-based course in Summer 2024
Student workload
Lectures, quided exercises and exam 40 h
Independent work and automatic tests 40 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information
Continuous feedback: tests in Moodle
Exam to pass
Grading exam
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2023 - 24.08.2023
Timing
20.11.2023 - 31.01.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 92
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Course is implemented between 20.11.2023.-31.1.2024
Materials
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo - Lehtola - Nieminen - Rantakaulio: Tekninen matematiikka 1 and in Lehtola - Rantakaulio: Tekninen matematiikka 2
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam schedules
Läpäisykoe Exam-studiossa aikavälillä 14.1. - 7.3.
Arvosanakoe viikolla 5, sen uusintakoe 1 viikolla 8 ja uusintakoe 2 viikolla 11.
Completion alternatives
Web-based course in Summer 2024
Student workload
Lectures, quided exercises and exam 40 h
Independent work and automatic tests 40 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information
Jatkuva palaute: automaattitestit
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2023 - 24.08.2023
Timing
16.10.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Virtual portion
1.5 op
Mode of delivery
50 % Contact teaching, 50 % Distance learning
Unit
School of Technology
Teaching languages
- Finnish
Seats
0 - 70
Degree programmes
- Bachelor's Degree Programme in Energy and Environmental Technology
Teachers
- Antti Kosonen
Scheduling groups
- TER23S1 (Size: 45. Open UAS: 0.)
- TER23SM (Size: 45. Open UAS: 0.)
Groups
-
ZJATER23S1Avoin amk, Energia- ja ympäristötekniikka , päivä
-
TER23S1Energia- ja ympäristötekniikka (AMK)
-
TER23SMEnergia- ja ympäristötekniikka (AMK)
-
ZJATER23SMAvoin amk, Energia- ja ympäristötekniikka , monimuoto
Small groups
- Scheduling group 1
- Scheduling group 2
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented 13.11.2023 - 4.2.2024.
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.
- Rantakaulio, A. & Lehtola, P. 2013. Tekninen matematiikka: 2. 1. uus. p. Tampere: Tammertekniikka.
- Henttonen, J., Peltomäki, J. & Uusitalo, S. 2003. Tekniikan matematiikka: 1. Helsinki: Edita.
Teaching methods
Lectures, guided exercises, independent work, exams.
Lectures will also be streamed online.
Guided exercises will be held at campus or online depending on the implementation of your degree programme.
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 5 (2024), depending on your degree programme.
The exam that determines the grade will be held for everyone during week 5 starting on January 29, 2024.
The first resit exam will be held
- on February 21, 2024 for the traditional-mode course
- on February 22, 2024 for the flexible-mode course
The second resit exam will be held
- on March 20, 2024 for traditional-mode course
- on March 21, 2024 for the flexible-mode course
International connections
-
Completion alternatives
Face-to-face, hybrid and online implementations are available in autumn and in spring. It is also possible to attend the course online during summer 2024.
Student workload
Calculatory workload: 3cr * 27h/cr = 81h
Weekly use of time:
Lectures 2 * 45 min
Exercises 2 * 45 min
Additionally:
- Exams approximately 4 h
- Independent work approximately 55 - 60 h
Content scheduling
More detailed schedule will be announced at the beginning of the course, but the topics will be covered roughly in the following order:
- Revision and Supplementation of Functions
- Exponential Functions
- Logarithms
- Trigonometric Functions
- Trigonometric Functions
- Limits and Continuity of Functions
Further information
Assessment is based on two-part final exam and tests / exercises.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
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
- Bachelor's Degree Programme in Construction Management
Teachers
- Kalle Niemi
Groups
-
UTIVERKKOInstitute of New Industry, online learning (mechanical, logistics and civil engineering)
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented 28.8. - 17.12.
Materials
Videos and written material in e-learning environment Moodle.
Recommended literature (in Finnish):
- Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen matematiikka 1
- Henttonen, Oinonen, Uusitalo: Tekniikan matematiikka 1
Teaching methods
Independent studying with videos, written learning material and exercises.
Exam schedules
The exam to pass the course can be taken in the EXAM studio.
The dates of the grading exam are announced on the Moodle page of the course.
Completion alternatives
Face-to-face or hybrid implementation in autumn or in spring. Online course in spring or in summer 2024.
Student workload
Calculatory workload:
27 h/op * 3op = 81 h
Of this approximately
- 32 h of studying the material
- 45 h of exercises
- 4 h for exams.
Content scheduling
A detailed schedule will be available in the e-learning environment when the course starts.
Further information
Summative assessment is based on a two-part final exam.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2023 - 24.08.2023
Timing
21.08.2023 - 03.12.2023
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 - 40
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Kalle Niemi
Groups
-
TLS23KMMLogistiikka - tutkinto-ohjelma (AMK)
-
ZJATLS23KMMAvoin amk, AMK-polut, Logistiikka, Monimuoto
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course will be carried 21.8.2023 - 12.11.2023.
Materials
Written material and video material on Moodle.
Teaching methods
Online-lessons, contact teaching, independent work.
Exam schedules
Ilmoitetaan ensimmäisessä tapaamisessa.
Completion alternatives
Independently conducted online course during autumn or spring. Face-to-face implementations are arranged in both autumn and spring.
Student workload
3 cr * 27 h/cr = 81 h.
Content scheduling
A more detailed schedule will be presented at the beginning of the course, but the content will be arranged more or less as follows:
1. Revision and Supplementation of Functions
2. Exponential Functions and Logarithms
3. Trigonometric Functions
4. Limits and Continuity of Functions
Further information
Assessment is based on two-part final exam and exercises.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2023 - 24.08.2023
Timing
21.08.2023 - 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 - 30
Degree programmes
- Bachelor's Degree Programme in Construction Management
Teachers
- Kalle Niemi
Teacher in charge
Kalle Niemi
Groups
-
ZJATRM23KMMAvoin amk, AMK-polut, Rakennusmestari, Monimuoto
-
TRM23KMMRakennusmestari (AMK)
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course will be carried 21.8.2023 - 12.11.2023.
Materials
Written material and video material on Moodle.
Teaching methods
Online-lessons, contact teaching, independent work.
Exam schedules
Ilmoitetaan ensimmäisessä tapaamisessa.
Completion alternatives
Independently conducted online course during autumn or spring. Face-to-face implementations are arranged in both autumn and spring.
Student workload
3 cr * 27 h/cr = 81 h.
Content scheduling
A more detailed schedule will be presented at the beginning of the course, but the content will be arranged more or less as follows:
1. Revision and Supplementation of Functions
2. Exponential Functions and Logarithms
3. Trigonometric Functions
4. Limits and Continuity of Functions
Further information
Assessment is based on two-part final exam and exercises.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2023 - 24.08.2023
Timing
01.08.2023 - 15.10.2023
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
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 Construction Management
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Pekka Varis
Groups
-
TSA23KMInsinööri (AMK), sähkö- ja automaatiotekniikka,monimuototeutus
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Opintojakso toteutetaan viikoilla 35 - 41 (28.8. - 13.10.2021)
Materials
Opintojakson kirjallinen materiaali sekä videomateriaali julkaistaan opintojakson oppimisympäristössä opintojakson alussa.
Teaching methods
Itsenäinen opiskelu videoluentojen avulla, viikottainen verkko-ohjaus
Exam schedules
Kokeen ajankohdat julkaistaan oppimisympäristössä opintojakson alussa. Kokeen voi tehdä paikan päällä tai etänä.
Student workload
verkko-ohjaukset 9 h
Itsenäiset harjoitukset 32 h
Itsenäinen opiskelu, kokeeseen valmistautuminen sekä koe 40 h
Further information
Opintoijakso arvioidaan kurssin lopulla pidettävällä kokeella. Viikottaisista kotitehtävistä saa kokeeseen lisäpisteitä.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
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 - 5
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
- Antti Kosonen
Teacher in charge
Antti Kosonen
Groups
-
LOGRAKVERKKOLogistiikan ja rakentamisen verkko-opetus
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented 01.05.2023 - 31.08.2023.
Materials
Videos and written material in e-learning environment Moodle.
Recommended literature (in Finnish):
- Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen matematiikka 1
- Henttonen, Oinonen, Uusitalo: Tekniikan matematiikka 1
Teaching methods
Independent studying with videos, written learning material and exercises.
Exam schedules
Exam dates will be published in Moodle at the beginning of the implementation.
Completion alternatives
Face-to-face, hybrid or online implementation in autumn 2023 or spring 2024.
Student workload
Calculatory workload:
27 h/op * 3op = 81 h
Of this approximately
- 32 h of studying the material
- 45 h of exercises
- 4 h for exams.
Content scheduling
A detailed schedule will be available in the e-learning environment when the course starts.
Further information
Summative assessment is based on a two-part final exam in which you can participate at Rajakatu campus or online.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022 - 05.01.2023
Timing
07.03.2023 - 30.04.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 60
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Kalle Niemi
Scheduling groups
- TLS22SA (Size: 35. Open UAS: 0.)
- TLS22SB (Size: 35. Open UAS: 0.)
Groups
-
TLS22S1Logistiikka - tutkinto-ohjelma (AMK)
-
ZJATLS22S1Avoin amk, Logistiikka, Päivä
Small groups
- TLS22SA
- TLS22SB
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Course is implemented between 30.3.2023 - 30.4.2023
Materials
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo - Lehtola - Nieminen - Rantakaulio: Tekninen matematiikka 1 and in Lehtola - Rantakaulio: Tekninen matematiikka 2
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam schedules
Ilmoitetaan ensimmäisellä tunnilla.
Completion alternatives
Web-based course in Summer 2023
Student workload
Lectures, quided exercises and exam 40 h
Independent work and automatic tests 40 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information
Jatkuva palaute: automaattitestit
Läpäisykoe
Arvosanakoe
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Timing
09.01.2023 - 24.02.2023
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented between 9.1.2023 and 24.2.2023.
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Alestalo, Lehtola, Nieminen, Rantakaulio - Tekninen matematiikka 1 (in Finnish)
- Henttonen, Peltomäki, Uusitalo - Tekniikan matematiikka 1 (in Finnish)
- 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
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
The estimated total workload is 81 hours, which is divided by approximately 20% to contact teaching and 80% for independent work.
Content scheduling
The course timetable is agreed on at the beginning of the course and then published in the e-learning environment.
Further information
Opintojaksoon liittyy kotitehtäviä, läpäisytestejä ja koe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (75 % oikein) perusasioihin liittyvät läpäisytestit. Korkeampi arvosana edellyttää kokeeseen osallistumista. Jotta kokeeseen voi osallistua, täytyy läpäisytestit olla suoritettu hyväksytysti.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 24.02.2023
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Kevätlukukauden 2023 ensimmäinen puolisko.
Materials
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 -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 Mat2 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 24.02.2023
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 - 140
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented between 9.1.2023 and 24.2.2023.
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Alestalo, Lehtola, Nieminen, Rantakaulio - Tekninen matematiikka 1 (in Finnish)
- Henttonen, Peltomäki, Uusitalo - Tekniikan matematiikka 1 (in Finnish)
- 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
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
The estimated total workload is 81 hours, which is divided by approximately 20% to contact teaching and 80% for independent work.
Further information
Opintojaksoon liittyy kotitehtäviä, välitestejä, läpäisytesti ja arvosanakoe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (80 % oikein) perusasioihin liittyvät läpäisytestit. Korkeampi arvosana edellyttää kokeeseen 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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 24.02.2023
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Two lessons (90min) per week during weeks 2-8.
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.
Exam schedules
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 24.02.2023
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Kevätlukukauden 2023 ensimmäinen puolisko.
Materials
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 -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 Mat2 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 24.02.2023
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
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented between 9.1. and 24.2.
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Alestalo, Lehtola, Nieminen, Rantakaulio - Tekninen matematiikka 1 (in Finnish)
- Henttonen, Peltomäki, Uusitalo - Tekniikan matematiikka 1 (in Finnish)
- 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.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 24.02.2023
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented between 9.1.2023 and 24.2.2023.
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Alestalo, Lehtola, Nieminen, Rantakaulio - Tekninen matematiikka 1 (in Finnish)
- Henttonen, Peltomäki, Uusitalo - Tekniikan matematiikka 1 (in Finnish)
- 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
Mahdollisuus tenttiä kurssikokeella opintojakson alussa.
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Content scheduling
The course timetable is agreed on at the beginning of the course and then published in the e-learning environment.
Further information
Opintojaksoon liittyy kotitehtäviä, välitestejä, läpäisytesti ja arvosanakoe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (80 % oikein) perusasioihin liittyvät läpäisytestit. Korkeampi arvosana edellyttää kokeeseen 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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 24.02.2023
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented between 9.1. and 24.2.
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Alestalo, Lehtola, Nieminen, Rantakaulio - Tekninen matematiikka 1 (in Finnish)
- Henttonen, Peltomäki, Uusitalo - Tekniikan matematiikka 1 (in Finnish)
- 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.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 19.05.2023
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
-
TLP23VKBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
-
TLP22S1Bachelor's Degree Programme in Purchasing and Logistics Engineering
-
ZJATLP22S1Avoin amk, Purchasing and Logistics Engineering, Päivä
-
TLP22VSBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
One lesson(90min) per week during weeks 2-8 and 11-16.
Materials
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Exam schedules
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 20h independent studying of theory
approx. 30h independent studying of exercises
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
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
- Antti Kosonen
Teacher in charge
Antti Kosonen
Groups
-
LOGRAKVERKKOLogistiikan ja rakentamisen verkko-opetus
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented 9.1.2023 - 19.5.2023.
Materials
Videos and written material in e-learning environment Moodle.
Recommended literature (in Finnish):
- Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen matematiikka 1
- Henttonen, Oinonen, Uusitalo: Tekniikan matematiikka 1
Teaching methods
Independent studying with videos, written learning material and exercises.
Exam schedules
Possible dates for exam / resit:
- 18.1.2023
- 8.2.2023
- 22.3.2023
- 12.4.2023
- 17.5.2023
- 31.5.2023
Completion alternatives
Face-to-face or hybrid implementation in spring. Online course in spring or in summer 2023.
Student workload
Calculatory workload:
27 h/op * 3op = 81 h
Of this approximately
- 32 h of studying the material
- 45 h of exercises
- 4 h for exams.
Content scheduling
A detailed schedule will be available in the e-learning environment when the course starts.
Further information
Summative assessment is based on a two-part final exam in which you can participate at Rajakatu campus or online.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Course is implemented between 28.11.2022 - 17.2.2023
Materials
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo - Lehtola - Nieminen - Rantakaulio: Tekninen matematiikka 1 and in Lehtola - Rantakaulio: Tekninen matematiikka 2
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam schedules
Läpäisykoe Exam-studiossa aikavälillä 23.1. - 10.3.
Arvosanakoe viikolla 7, sen uusintakoe 1 viikolla 10 ja uusintakoe 2 viikolla 13.
Completion alternatives
Web-based course in Summer 2023
Student workload
Lectures, quided exercises and exam 40 h
Independent work and automatic tests 40 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information
Jatkuva palaute: automaattitestit
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 19.05.2023
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 - 50
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Kalle Niemi
Teacher in charge
Kalle Niemi
Groups
-
ZJATLS22SMMAvoin amk, Logistiikka, Monimuoto
-
TLS22SMMLogistiikka - tutkinto-ohjelma (AMK)
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course will be carried out 9.1.2023 - 26.4.2023.
Materials
Written material and video material prepared by teacher.
Teaching methods
Online-lessons, contact teaching, independent work.
Exam schedules
Will be announced at the first meeting of the course.
Completion alternatives
Independently conducted online course during autumn or spring. Face-to-face implementations are arranged in both autumn and spring.
Student workload
3 cr * 27 h/cr = 81 h.
Content scheduling
A more detailed schedule will be presented at the beginning of the course, but the content will be arranged more or less as follows:
1. Revision and Supplementation of Functions
2. Exponential Functions and Logarithms
3. Trigonometric Functions
4. Limits and Continuity of Functions
Further information
Assessment is based on two-part final exam and exercises.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 26.02.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 65
Degree programmes
- Bachelor's Degree Programme in Electrical and Automation Engineering
Teachers
- Kalle Niemi
Teacher in charge
Ida Arhosalo
Groups
-
ZJATSA22S1Avoin amk, Sähkö- ja automaatiotekniikka, Päivä
-
TSA22SR1Sähkö- ja automaatiotekniikka (AMK)
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Course is implemented between 9.1.2023 - 24.2.2023
Materials
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo - Lehtola - Nieminen - Rantakaulio: Tekninen matematiikka 1 and in Lehtola - Rantakaulio: Tekninen matematiikka 2
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam schedules
Ilmoitetaan ensimmäisellä tunnilla.
Completion alternatives
Web-based course in Summer 2023
Student workload
Lectures, quided exercises and exam 30 h
Independent work and automatic tests 51 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information
Jatkuva palaute: automaattitestit
Läpäisykoe
Arvosanakoe
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 26.02.2023
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
- Kalle Niemi
Teacher in charge
Ida Arhosalo
Groups
-
TSA22SR2Sähkö- ja automaatiotekniikka (AMK)
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
21.11.2022 - 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
- 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
- Kalle Niemi
Teacher in charge
Ida Arhosalo
Groups
-
TAR22S1Bachelor's Degree Programme in Automation and Robotics
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Materials
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Exam schedules
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 20h independent studying of theory
approx. 30h independent studying of exercises
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2022 - 25.08.2022
Timing
31.10.2022 - 18.12.2022
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 - 60
Degree programmes
- Bachelor's Degree Programme in Energy and Environmental Technology
Teachers
- Antti Kosonen
Scheduling groups
- Päiväryhmä TER22S1 (Size: 50. Open UAS: 0.)
- Monimuotoryhmä TER22SM (Size: 50. Open UAS: 0.)
Groups
-
TER22S1Energia- ja ympäristötekniikka (AMK)
-
TER22SMEnergia- ja ympäristötekniikka (AMK)
-
ZJATER22S1Avoin amk, Energia- ja ympäristötekniikka
-
ZJATER22SMAvoin amk, Energia- ja ympäristötekniikka , monimuoto
Small groups
- Pienryhmä 1
- Pienryhmä 2
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented 31.10.2022 - 18.12.2022.
Lectures will also 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.
- Rantakaulio, A. & Lehtola, P. 2013. Tekninen matematiikka: 2. 1. uus. p. 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 50, depending on the implementation of your degree programme.
A grade-determining exam will take place during week 50.
First resit 18.1.2023
Second resit 8.2.2023
Completion alternatives
Face-to-face, hybrid and online implementations are available in autumn and in spring. 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. Revision and Supplementation of Functions
2. Exponential Functions
3. Logarithms
4. Trigonometric Functions
5. Trigonometric Functions
6. Limits and Continuity of Functions
Further information
Assessment is based on two-part final exam and exercises.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
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 - 20
Degree programmes
- Bachelor's Degree Programme in Logistics
- Bachelor's Degree Programme in Construction and Civil Engineering
Teachers
- Antti Kosonen
Teacher in charge
Antti Kosonen
Groups
-
LOGRAKVERKKOLogistiikan ja rakentamisen verkko-opetus
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented 29.8. - 18.12.
Materials
Videos and written material in e-learning environment Moodle.
Recommended literature (in Finnish):
- Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen matematiikka 1
- Henttonen, Oinonen, Uusitalo: Tekniikan matematiikka 1
Teaching methods
Independent studying with videos, written learning material and exercises.
Exam schedules
Possible dates for exam / resit:
- 9.11.2022
- 30.11.2022
- 14.12.2022
- 18.1.2023
- 8.2.2023
Completion alternatives
Face-to-face or hybrid implementation in autumn or in spring. Online course in spring or in summer 2023.
Student workload
Calculatory workload:
27 h/op * 3op = 81 h
Of this approximately
- 32 h of studying the material
- 45 h of exercises
- 4 h for exams.
Content scheduling
A detailed schedule will be available in the e-learning environment when the course starts.
Further information
Summative assessment is based on a two-part final exam in which you can participate at Rajakatu campus or online.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2022 - 25.08.2022
Timing
29.08.2022 - 13.11.2022
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 - 40
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Antti Kosonen
Teacher in charge
Antti Kosonen
Groups
-
ZJA22KTPMLAvoin AMK, tekniikka, Logistiikka, monimuoto
-
ZJA21STPMLAvoin amk, tekniikka, Logistiikka monimuoto
-
TLS22KMMLogistiikan tutkinto-ohjelma (AMK)
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course will be carried out 29.8.2022 - 13.11.2022.
Materials
Written material and video material prepared by teacher.
Teaching methods
Online-lessons, contact teaching, independent work.
Exam schedules
Final exam in two parts during week 45.
Completion alternatives
Independently conducted online course during autumn or spring. Face-to-face implementations are arranged in both autumn and spring.
Student workload
3 cr * 27 h/cr = 81 h.
Content scheduling
A more detailed schedule will be presented at the beginning of the course, but the content will be arranged more or less as follows:
1. Revision and Supplementation of Functions
2. Exponential Functions and Logarithms
3. Trigonometric Functions
4. Limits and Continuity of Functions
Further information
Assessment is based on two-part final exam and exercises.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.08.2022 - 25.08.2022
Timing
15.08.2022 - 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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Course is implemented between 28.11.2022.-11.2.2023
Materials
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo - Lehtola - Nieminen - Rantakaulio: Tekninen matematiikka 1 and in Lehtola - Rantakaulio: Tekninen matematiikka 2
Teaching methods
Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.
Exam schedules
Läpäisykoe Exam-studiossa aikavälillä 16.1. - 10.3.
Arvosanakoe viikolla 6, sen uusintakoe 1 viikolla 10 ja uusintakoe 2 viikolla 13.
Completion alternatives
Web-based course in Summer 2023
Student workload
Lectures, quided exercises and exam 40 h
Independent work and automatic tests 40 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information
Jatkuva palaute: automaattitestit
Läpäisykoe
Arvosanakoe
Bonustehtävä
Avoin AMK 5
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 25.02.2022
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Kevätlukukauden 2022 ensimmäinen puolisko.
Materials
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 -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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 25.02.2022
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Kevätlukukauden 2022 ensimmäinen puolisko.
Materials
Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 -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)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 25.02.2022
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
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented between 10.1.2022 and 25.2.2022
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Alestalo, Lehtola, Nieminen, Rantakaulio - Tekninen matematiikka 1 (in Finnish)
- Henttonen, Peltomäki, Uusitalo - Tekniikan matematiikka 1 (in Finnish)
- 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 2022
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Further information
Opintojaksoon liittyy kotitehtäviä, läpäisytestejä ja koe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (80 % oikein) perusasioihin liittyvät läpäisytestit (3 kpl). Korkeampi arvosana edellytttää kokeeseen osallistumista. Jotta kokeeseen voi osallistua, täytyy läpäisytestit olla suoritettu.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 25.02.2022
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented between 10.1.2022 and 25.2.2022
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Alestalo, Lehtola, Nieminen, Rantakaulio - Tekninen matematiikka 1 (in Finnish)
- Henttonen, Peltomäki, Uusitalo - Tekniikan matematiikka 1 (in Finnish)
- 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 2022
Student workload
The estimated workload is 81 hours, which is divided approximately fifty - fifty between contact teaching and independent work.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Further information
Opintojaksoon liittyy kotitehtäviä, läpäisytestejä ja koe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (80 % oikein) perusasioihin liittyvät läpäisytestit (3 kpl). Korkeampi arvosana edellytttää kokeeseen osallistumista. Jotta kokeeseen voi osallistua, täytyy läpäisytestit olla suoritettu.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 25.02.2022
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
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 110
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Sirpa Alestalo
- Kalle Niemi
Groups
-
TTV21SMTieto- ja viestintätekniikka (AMK)
-
ZJA21STPMTVAvoin amk, tekniikka, Tieto- ja viestintätekniikka, verkko
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
The course is implemented between 10.1.2022 and 11.3.2022
Materials
Course material consists of written material and video material available in the e-learning environment.
Recommended literature:
- Alestalo, Lehtola, Nieminen, Rantakaulio - Tekninen matematiikka 1 (in Finnish)
- Henttonen, Peltomäki, Uusitalo - Tekniikan matematiikka 1 (in Finnish)
- 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 2022
Student workload
The estimated workload is 81 hours, which is divided approximately twenty- eighty between contact teaching and independent work.
Content scheduling
The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.
Further information
Opintojaksoon liittyy kotitehtäviä, läpäisytestejä ja koe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (75 % oikein) perusasioihin liittyvän läpäisytestin. Korkeampi arvosana edellytttää kokeeseen osallistumista. Jotta kokeeseen voi osallistua, täytyy läpäisytestit olla suoritettu.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 25.02.2022
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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Two lessons (90min) per week during weeks 2-8.
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.
Exam schedules
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 50 h for independent studying.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 29.04.2022
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 Logistics
Teachers
- Ville Sivil
Teacher in charge
Antti Kosonen
Scheduling groups
- TLS21SA (Size: 40. Open UAS: 0.)
- TLS21SB (Size: 40. Open UAS: 0.)
Groups
-
ZJA21STPPLOAvoin amk, tekniikka, Logistiikka päivä
-
TLS21S1Logistiikan tutkinto-ohjelma (AMK)
Small groups
- TLS21SA
- TLS21SB
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Course is implemented between 10.1.2022 - 27.2.2022.
Materials
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo - Lehtola - Nieminen - Rantakaulio: Tekninen matematiikka 1
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.
Student workload
Lectures, quided exercises and exam 40 h
Independent work and automatic tests 41 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 29.03.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- Finnish
Seats
0 - 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
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Course is implemented between 10.1.-25.2.2022.
Materials
Videos in the learning environment, text files, automatic tests
Extra material in Alestalo - Lehtola - Nieminen - Rantakaulio: Tekninen matematiikka 1 and in Lehtola - Rantakaulio: Tekninen matematiikka 2
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, quided exercises and exam 40 h
Independent work and automatic tests 40 h
Content scheduling
Will be agreed on the first contact lesson of the course.
Further information
Avoin AMK 5
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021 - 23.01.2022
Timing
10.01.2022 - 25.02.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
Campus
Main Campus
Teaching languages
- English
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Kalle Niemi
Teacher in charge
Ida Arhosalo
Groups
-
TLP21S1Bachelor's Degree Programme in Purchasing and Logistics Engineering
-
TLP21VSBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
-
ZJA21STPPLPAvoina amk, tekniikka, Logistics and purchasing, päivä
-
TLP22VKBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
One lesson(90min) per week during weeks 2-16.
Materials
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Exam schedules
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 20h independent studying of theory
approx. 30h independent studying of exercises
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021 - 09.01.2022
Timing
10.01.2022 - 20.05.2022
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 - 20
Degree programmes
- Bachelor's Degree Programme in Electrical and Automation Engineering
Teachers
- Antti Kosonen
Teacher in charge
Antti Kosonen
Groups
-
TSA22KMInsinööri (AMK), sähkö- ja automaatiotekniikka,monimuototeutus
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Opintojakso toteutetaan 7.3.2022 - 7.5.2022.
Materials
Kurssilla saat käyttöösi opintojaksoa varten laaditut oppimateriaalit (kirjallinen- ja videomateriaali)
Teaching methods
Verkko-opetus, kontaktiopetus, itsenäinen työsentely.
Exam schedules
Läpäisykoe pe 6.5.
Arvosanakoe la 7.5.
Uusintojen ajankohdat sovitaan aloitustapaamisessa.
Completion alternatives
Verkkototeutus kesällä 2022.
Student workload
3op * 27h/op = 81h
Further information
Osaamista arvioidaan kaksiosaisella loppukokeella.
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Timing
03.01.2022 - 31.05.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Contact teaching
Unit
School of Technology
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
- Antti Kosonen
Groups
-
ZJA21KTPMLAvoin AMK, tekniikka, AMK-polut, logistiikka
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Opintojakso toteutetaan 7.3.2022 - 7.5.2022.
Materials
Kurssilla saat käyttöösi opintojaksoa varten laaditut oppimateriaalit (kirjallinen- ja videomateriaali)
Teaching methods
Verkko-opetus, itsenäinen työsentely.
Completion alternatives
Verkkototeutus kesällä 2022.
Student workload
3op * 27h/op = 81h
Further information
AVOIN AMK
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
02.08.2021 - 31.05.2022
Timing
30.08.2021 - 30.08.2022
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 - 15
Degree programmes
- Bachelor's Degree Programme in Logistics
Teachers
- Antti Kosonen
Teacher in charge
Antti Kosonen
Groups
-
ZJK22KTKorkeakoulujen välinen yhteistyö, TEKN
-
ZJA21STAvoin AMK, tekniikka
-
LOGAKTIIVILogistiikan aktiivitoteutukset
-
ZJA22KTAvoin AMK, tekniikka
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
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.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
E-learning course. Implementation starts 30.8.
Materials
Written material and video material.
Teaching methods
The course will be conducted independently in an e-learning environment. The course material consists of written and and video material, exercises and a final exam.
Exam schedules
Schedule will be announced in the e-learning environment
Student workload
3 cr * 27 h/cr = 81 h.
Further information
Avoin AMK syksy 5
Avoin AMK polku kevät 15
Avoin AMK kevät 5
Avoin AMK kesä 10
CampusOnline 20
Evaluation scale
0-5
Assessment criteria, satisfactory (1)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Assessment criteria, good (3)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.