Syllabus
Fourier series, Bessel inequality and Parseval equality, differentiation and integration of Fourier series.
Hilbert space, abstract Fourier series in Hilbert space, orthogonal systems of polynomials (Laguerre, Hermite, Tschebyschew). Operators in Hilbert space.
Complex analysis, Cauchy theorem, Cauchy formula, residual theorem.
Fourier transform and its applications.
Introduction to the theory of PDEs. Wave equation, heat equation, Laplace-Poisson equation.
Annotation
Fourier series, both classical and abstract. Hilbert space. Basic course on complex analysis. Fourier transform,
Basic theory of PDEs.