Credit Points: 2.5
Prerequisites: Differential and Integral Calculus; Ordinary Differential Equations;
Complex Functions (concurrent)
Orthonormal systems and generalized Fourier series. Various forms of the harmonic Fourier series. Bessel and Legender functions. Partial sums, Dirichlet integral. The Riemann-Lebesgue lemma and Riemann localization. Fourier series with two independent variables. Convergence: Dirichle-Jordan, Dini, and Lipschits conditions. Uniform convergence. Convergence near discontinuities. Gibbs phenomena. Convergence rate and differentiability. Series integration and differentiation. Separable Hilbert spaces. Bases. Riesz-Fischer theorem. The best approximation problem. Bessel inequality. Parseval identity. Completeness of the trigonometric set. Properties of the Fourier transform in L1 and L2. Laplace transform.