# TMA4135 Mathematics 4D autumn 2018

## Course Description

The official course description can be found here.

The course is divided into two parts:

#### Laplace transforms and Fourier analysis

On this part you will learn about Laplace transform (a smart way to transform differential equations into algebraic ones, that are more easy to solve). You will learn about Fourier series, a technique for expressing simple functions as a sum of sinus- and cosinus signals, as well as its extension, the Fourier transforms. These topics have applications in signal processing, image compression and a lot of other areas. We will also discuss functions of several variables, and how to solve partial differential equations, e.g. the heat equations, by Fourier series.

This part is lectured by Xu Wang, in English.

#### Numerical methods

Most of the mathematical equations and expressions encountered in real life applications can not be solved by pen and paper. Instead, we search for approximate solutions, found by the use of numerical algorithms and implemented on computers. In this course, we will look at numerical algorithms for solving nonlinear algebraic as well as ordinary and partial differential equations. We will also study how functions can be approximated by polynomials, and how this can be used to find approximations to integrals. Implementation and testing are indispensable elements when studying numerical methods. The lecture material in this part of the course is given as Jupyter notebooks, which are interactive web based notes containing both mathematical text and executable python code.

This part is lectured by Anne Kværnø, in Norwegian.

### Office hours

Monday 10:30-11:45

### Lecture plan

• Monday 12:15-14:00 in S3 SB1
• Friday 10:15-12:00 in S2 SB1

For the exercise hours, see the timetable.

## Teaching material:

• Textbook: Advanced Engineering Mathematics by Erwin Kreyszig, 10th edition, John Wiley & Sons, 2011.
• Lecture notes
• Jupyter notebooks (will be made available when the numerics part of the course starts).

## Final exam

• December 14, 2018.