# Higher Mathematics IV

Copyright: © privateUpon successful completion of the course, the students are proficient in the theory and calculus of complex functions and their application in the calculation of advanced and oscillating integrals. In the part on functional analysis, physics students learn the mathematical foundations of theoretical physics and how to work with the related concepts and tools.

Content

The course is split in two parts. Both electrical engineering and physics students are required to complete the one on complex analysis. The part on functional analysis is only compulsory for physics students.

Topics

Complex analysis: holomorphic functions, Möbius transformations, conformal mappings, complex integration, Cauchy integral theorem, Laurent series, residue theorem

Functional analysis: Hilbert spaces, bounded and self-adjoint operators, elementary spectral theory, Lebesgue integral, Fourier transform, distributions, aspects of partial differential equations

Prerequisites and assessment:

Electrical Engineering:

In order to take the course, you must have previously been enrolled in HM1, HM2 and HM3. The assessment consists of a 90 minute written exam.

Physics:

There are no prerequisites for the module. Admission to the module examination is acquired by written homework. An additional admissions requirement for the examination is regular participation in the exercise classes. The assessment consists of 90 minute written exam whose grade determines 100% of the grade in the module.

Literature

- K. Meyberg, P. Vachenauer: Höhere Mathematik 1, 2, Berlin, 2001
- K. Burg, H. Haf, R. Wille: Höhere Mathematik für Ingenieure, III (Gewöhnliche Differentialgleichungen), IV (Vektoranalysis, Funktionentheorie), 2002, 1994,