### Mathematical Theory of Maxwell's Equations (Summer Semester 2009)

- Lecturer: Prof. Dr. Andreas Kirsch
- Classes: Lecture (1562)
- Weekly hours: 4

Schedule | ||
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Lecture: | Monday 9:45-11:15 | Seminarraum 31 |

Wednesday 9:45-11:15 | Seminarraum 31 |

Lecturers | ||
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Lecturer | Prof. Dr. Andreas Kirsch | |

Office hours: by apointment | ||

Room 0.011 Kollegiengebäude Mathematik (20.30) | ||

Email: Andreas.Kirsch@kit.edu |

**Content:** Electromagnetic wave propagaition is modeled by a system of two partial differential equations for the electric and magnetic fields E and H, the Maxwell system. This will be the starting point of our lecture. We will consider time-harmonic fields (i.e. periodic in time) solely. The mathematical treatment of the Maxwell system will extensively make use of Sobolevspaces, which will be introduced at the beginning of the lectures. Then we will consider cavity problems, i.e. boundary value problems in bounded domain. Finally, we will treat scattering problems for bounded objects.

**Prerequisits:** Vordiplom in Mathematics, Physics or in Engineering

Basic knowledge of functional analysis is needed, in particular the notions of normed spaces, Hilbert spaces including their most important examples (), linear and bounded or compact operators, the representations theorem of Riesz. Further facts on functional analysis will be derived during the course.

# Lecture Notes

We will regularily update the lecture notes of this course. Here is part 1.

# References

D. Colton, R. Kress: Integral Equation Methods in Scattering Theory. Wiley, 1983.

D. Colton, R. Kress: Inverse Acoustic and Electromagnetic Scattering Theory (2nd Ed.). Springer, 1998.

P. Monk: Finite Element Methods for Maxwell's Equations. Oxford University Press 2003.