Mathematics 2Laajuus (5 cr)

Objective

The students can define the inverse function and the combined function for given functions. The students can find the most suitable regression curve for a given test data and they understand the meaning of the correlation coefficient. The students can handle geometric and an arithmetic series. The students can define the limit of a sequence of numbers or a function. The students master the basics of the derivative and integral calculus for real functions and they can use their knowledge in applications. The students know the basic calculations with complex numbers and matrices.

Content

Combined functions and inverse function, interpolation and extrapolation and regression and correlation coefficient. Limit values and continuation of functions. Basics of polynome-, rational-, root-, power-, exponent-, and logarithm functions and also differential and integral calculus of trigonometric functions. Complex numbers. Elements of matrix calculation. The exercises include both basic tasks and applications from the field of mechanical engineering. Use of mathematical computer programs in the applications of differential and integral calculus.

Qualifications

The students can form expressions, equations or functions. The students can handle expressions and solve equations by hand, using a calculator or mathematical computer programs. The students master the writing of mathematical expressions and also the use of necessary information technological tools. The students understand the concept of a function, they can draw and analyze graphs of functions and form equations of functions from graphs.

Assessment criteria, satisfactory (1)

Very good (4-5): The student has a clear overall idea of the subject and the competence to apply independently the derivative and integral calculus to simple scientific problems.
Good (3): The student masters the essential learning objectives of the course: limit values, derivative and integral calculus.
Satisfactory (1-2): The student masters inadequately the learning objectives of the course: the idea of the subject is fragmentary