Higher Mathematics IV

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Upon completion of the course, the students are proficient in the theory and calculus of complex functions and their application to the computiation of advanced and oscillating integrals. In the part on functional analysis, physic students will learn the mathematical foundations for theoretical physics; as a result they are able to deal with the relevant terms.

Topics

The course is split in two parts. Both electrical engineering and physics student are required to enroll in the one on complex analysis. On the other hand there is the part on functional analysis, this one is only compulsory for physics students.

Among others, the following topics are covered:

Complex analysis:

holomorphic functions, Möbius transformations, comformal mappings, complex integration, Cauchy integral theorem, Laurent series, reidue theorem

Functional analysis:

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

Prerequisites/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 exam.

Physics:

There are no prerequisites for the module. Admission to the module eyamination is acquired by written homework. An additional admission requirement for the module examination is regular presence in the exercise classes. The assissment consists of 90 minute exam.

Literature

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