PHYS 612 Mathematical Methods of Theoretical Physics II

Fourier series. Fourier, Laplace and other integral transforms. Partial differential equations (PDE) and boundary-value problems. First-order PDE in two independent variable, linear second-order PDE in two and three independent variables. Generalized functions and distributions. Integral representations and Green's functions. Applications to Laplace, Poisson, diffusion and wave equations.