Modul

The module examination is carried out by one oral examination (approx. 30 minutes).

By successfully participating in the problem classes by correctly completing 60% of the programming exercise assignments, students will obtain a bonus to the grade of the oral examination. This bonus amounts to an improvement of the grade to the next marking step (a decrease by 0.3 or 0.4, respectively), if the original grade is between 4.0 and 1.3.

Students are able to name and describe basic methods for numerically solving linear integral equations of the second kind, such as degenerate kernel approximation, the Nyström method, collocation method and Galerkin method, as well as their underlying principles such as interpolation and numerical integration. They are able to apply these methods for numerically solving integral equations  and to implement concrete examples on a computer. Students are able to state convergence results concerning these methods and have mastered the application of methods of proof for such results. They can independently derive corresponding results for simple variations of these methods and perform the analysis of the convergence behavior for specific applications.

None

• Boundary integral operators
• Interpolation
• Quadrature formulae
• Approximation by degenerate kernel functions
• Nyström methods
• Projection methods

Numerical Analysis I

Integral Equations

Total workload: 240 hours

Attendance: 90 h

• lectures, problem classes and examination

Self studies: 150 h

• increased understanding of module content by wrapping up lectures at home
• work on exercises
• increased understanding of module content by self study of literature and internet research
• preparing for the examination