Special Functions. Bessel functions; integral representations; asymptotic expansions. Examples of applications in scattering theory. Hypergeometric functions; integral representations; confluent hypergeometric functions. Laplace and Fourier transforms. Gibbs phenomenon. Integral equations. Conformal mapping, and solution of two-dimensional potential problems. Riemann sphere. Introduction to tensor analysis; general coordinate transformations; covariant differentiation, general relativity. Some introductory group theory; orthogonal groups and their representations; spherical harmonics.