Analyysin perusteet (5 cr)

Evaluation scale

0-5

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 fundamentals 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. The objectives may differ a little depending on the degree programme.

Content

Combined functions and the inverse function, interpolation and extrapolation and also regression and correlation coefficient. Sequences of numbers and series. The limits and continuity of functions. Basics of differential and integral calculus of polynome-, rational-, root-, power-, exponent and logarithmic and trigonometric functions. Complex numbers. The elements of matrix calculation. The exercises include both basic tasks and applications from the field of mechanical engineering. Use of mathematical computer programs in applications of differential and integral calculus. The contents may vary a little depending on the degree programme.

Materials

Lehtola, Rantakaulio: Tekninen matematiikka 2, Tammertekniikka, 2004.

Completion alternatives

2 intermediate exams Deriving exam (exemption exam) Independent tasks (extra points, may raise the grade) Group tasks (extra points, may raise the grade)

Student workload

Lectures and calculation exercises70 h Independent work65 h Total 135 h

Assessment criteria, satisfactory (1)

Excellent (5) the students master most of the concepts and methods and they can apply them independently.
Good)(3-4)the students master some concepts and methods and they can apply them.
Satisfactory (1-2) the students understand some concepts and methods.

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 understand the concept of a function and they can draw and analyse graphs of functions and form the equation of a function from a graph.