6. Numerical analysis, scientific computing, and visualization.
The two basic courses provide a rigorous introduction to the most important strategies and concepts of modern numerical mathematics. The courses can be taken independently from each other. The first semester focuses mainly on numerical methods for ordinary differential equations, but also on deepening the knowledge in numerical linear algebra, especially regarding iterative methods for large systems. The second semester gives an introduction to partial differential equations from fundamental theory to modern numerical concepts.

Prerequisites: Non-linear systems of equations, best approximation, linear regression, hermite interpolation, numerical quadrature and initial value problems for ODEs.

Outline of the contents:

• Numerical methods for ODEs and numerical linear algebra
◦ stiff initial value problems and stability
◦ implicit Runge-Kutta and multistep methods
◦ numerical methods for DAEs
◦ iterative solution of linear equations and eigenvalue problems