Contents: first and second order differential equation; Wroskian; series solutions; ordinary and singulars points. Orthogonal eigenfunctions and Sturm-Liouville theory. Complex analysis, contour integration. Integral representation. Aymptotic expansions. Methods of stationst phase and steepest descent. Generalased functions. Special Functions. Bessel functions; Hypergeometric functions; Laplace and Fourier transforms. Gibbs phenomenon. Integral equations. Conformal mapping. Reimann sphere. Tensor analysis. Introduction to group theory. Spherical harmonics. |