Mathematics 4D - Differential equations and Fourier analysis

Partial derivatives. The Laplace transform with applications to solving ordinary differential equations and integral equations. Fourier series and the Fourier transform with applications to solving linear partial differential equations. Discrete Fourier transform. Numerical methods: Interpolation, differentiation, and integration. Methods for solving linear and non-linear equations. Runge-Kutta methods for solving systems of ordinary differential equations. Difference methods for solving partial differential equations. Introduction to computational tools with examples.

1. Knowledge. The student is able to recognize, understand and apply concepts and methods from the theory of Fourier series, Fourier transformation, Laplace transformation, ordinary and partial differential equations and numerical solution of systems of equations and differential equations.

2. Skills. The student is able to apply his or her knowledge of Fourier theory, ordinary and partial differential equations and numerical methods to formulate and solve problems in mathematics and the natural sciences/technology, if necessary with the additional aid of mathematical software.

Lectures and compulsory exercises. The lectures may be given in English.