IR201305 Calculus 2 (Matematiske metoder 2)

IR 101201 Calculus 1 (Matematiske metoder I)

After completion of the course the students should
- be able to do power series, Taylor series and Fourier series
- be able to draw graphs and classify extreme values for functions of two variables
- be able to do mathematical models using partial differentiation and differentials
- be able to find the Laplace transform of a function and be familar with the transfer function
- be familar with applications using Laplace transform and the invers transform
- be able to solve problems using CAS (computer algebra system).

Power series and Fourier series:
- Convergens, interval and radius of convergens. The ratio test.
- Taylor polynom and Taylor series.
- Fourier series of periodic functions.
- Fourier sine and cosine series.
- Finding Taylor and Fourier series using CAS (computer algebra system).
Functions of several variables:
- Describe and sketch the graph of functions of two variables.
- Partial derivatives, differentiable function and total differensial.
- Local and global extreme points and values.
- Use of CAS to draw graphs and calculate extreme values.
The Laplace transform:
- The Laplace transform and the invers transform.
- The transfer function and how to use this function modelling complex systems.
- Use of the Laplace transform to solve linear differential equations and systems of differential equations.
- Use of general formulas and CAS to find the Laplace transform and the invers transform.

Lectures and problem solvings

At the beginning of the course the professor can decide if the students have to do some obligatory exercises

3-hour written exams