Vector spaces. Bases. Linear transformations. Euclidean spaces. Topology of Euclidean spaces. Mean convergence. Fourier series. Convergence of Fourier series. Distributions. Weak convergence. Fourier transform. Orthogonal polynomial series. Boundary value problems. Sturm–Liouville problem. Eigenvalues and eigenvectors. Green’s function. Singular systems. Partial differential equations. Separation of variables: wave, heat, and Laplace equations. Laplace equation in rectangular, cylindrical, and spherical coordinates. Bessel functions and spherical harmonics.

Credits: 3.0 (three)