Syllabus
1. Fourier series
Trigonometric polynomials and series. Riemann-Lebesgue lemma, Riemann theorem on localization, Dirichlet kernel, pointwise properties of Fourier series, Fourier series in Hilbert spaces, Bessel inequality and Parseval equality. Orthogonal systems of polynomials (Legendre, Hermite, Chebyshev), eigenfunctions of differential operators. 2. Introduction to the complex analysis:
Holomorfic function, Cauchy-Riemann equations, line integral in the complex domain, primitive function. Cauchy theorem, Cauchy formula, Liouville theorem. Taylor series, function holomorfic between circular contours, isolated singularities, Laurent series. Residue and Residue theorem. 3. Fourier transform of functions
Definition and basic properties. Schwartz space, L1 and L2 theory, inversion theorems, convolution, application to ODE and PDE.
Annotation
Basic mathematics course for 2nd year students of physics. Prerequisities: Mathematics for physicists I, NMAF061.