First order equations, Lagrange's method for quasilinear equations, Cauchy's problem. Linear second order equations in 2 and 3 variables, ellipitc, hyperbolic and parabolic types. Solution by separation of variables. Poisson's equation, boundary-value problems with Dirichlet, Neumann and mixed conditions. Green's function. The wave equation and the heat equation, physical interpretation, initial conditions, solution methods.
