Mathematics 4K - Complex analysis, differential equations and Fourier analysis

Complex functions, complex integration, Laurent series and calculation of residues. The Laplace transform with applications to solving ordinary differential equations and integral equations. Introduction to linear second order partial differential equations. Fourier series and the Fourier transform with applications to solving linear partial differential equations.

1. Knowledge. The student is able to recognize, understand and apply concepts and methods from complex function theory, the theory of Fourier series, Fourier transformation and Laplace transformation, and linear second order partial differential equations. In particular in connection with the solution of ordinary and partial differential equations.

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

Lectures, compulsory exercises. Parts of the course may be lectured in English.