Course information

Fourier Series. Sturm-Lioville problems. Fundamental differential equations in Mathematical Physics (Laplace, wave equation and heat equation) in one,two and three dimensions. Construction of the equations as a modeling process via the fundamental physical laws. Linear, semilinear and quasilinear partial differential equations of first order. The method of characteristic curves. Blow up of solutions. Classification of Partial Differential equations of second order (elliptic, parabolic and hyperbolic). Well posed boundary value problems. The problems of Dirichlet, Newmann and Robin, which incorporate the boundary conditions. The separation of variables as a significant methodology for the solution of boundary value problems in several geometrical configurations. Fourier and Laplace transform in solving Pdes. Complex variables: Conformal mapping. Mobius and Schwartz-Cristoffel transformations. Mathematical theory of two dimensional fluid mechanics via complex analysis.