Modul
Numerical Methods for Integral Equations [M-MATH-102930]
Credits
8Recurrence
UnregelmäßigDuration
1 SemesterLanguage
Level
5Version
1Responsible
Organisation
- KIT-Fakultät für Mathematik
Part of
Bricks
Identifier | Name | LP |
---|---|---|
T-MATH-105901 | Numerical Methods for Integral Equations | 8 |
Competence Certificate
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.
Competence Goal
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.
Prerequisites
None
Content
- Boundary integral operators
- Interpolation
- Quadrature formulae
- Approximation by degenerate kernel functions
- Nyström methods
- Projection methods
Recommendation
Numerical Analysis I
Integral Equations
Workload
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