Analysis III E 1100-2Ind14

The Analysis IIIE is a continuation of the Analysis I and II E. The material covers the following issues
1. Elements of differential geometry: the concept of a submerged surface, tangent vectors, tangent space, covectors on the surface, vector fields and forms, outer product, polyforms, external differential, Poincare lemma, integration of differential forms, Stokes' theorem
2. Elements of complex analysis: differentiation in the complex sense, holomorphic functions, Taylor series, Laurent series, the concept of residuum, integration by the residua method, residuum at infinity, RUnge theorem, Gamma function.
3. Elements of distribution theory: sample functions, distributions, operations on distribution, convergence of the distribution sequence, compact carrier distributions, Fourier transform of functions, Fourier transform of distributions.