Applied Mathematics 3

Course content

Analysis: line, surface and volume integrals (discussion of work, flows, circulations); integral theorems of Gauß and Stokes (transformation of differential equations into integral equations); partial differential equations using the examples of wave and heat conduction equations; solution by separation and Fourier expansion; solution by Fourier transform.
Numerical methods: error problems in numerics; solution of systems of linear equations (direct, indirect methods); zeros of transcendental functions (Newton, bisection method, ...); quadrature (numerical integration); solution of ordinary differential equations (Runge-Kutta method); approximation of point sets (fitting of curves, least squares); solution of partial differential equations using the example of the finite difference method for the heat conduction equation.

Learning outcomes

Students learn how to apply mathematical methods to subject-specific tasks and calculations.

Recommended or required reading and other learning resources / tools

L. Papula: Mathematik für Ingenieure und Naturwissenschaftler
E. Kreyszig: Advanced Engineering Mathematics
Bronstein, Semendjajew: Taschenbuch der Mathematik

Mode of delivery

Integrated course

Prerequisites and co-requisites

Modules: Applied Mathematics 2; Informatics 3

Assessment methods and criteria

According to examination regulations