Partial Differential Equations

Linear and quasi-linear first order partial differential equations

Method of characteristics

Second order linear equations in two variables and their classification

Cauchy, Dirichlet and Neumann problems

Solutions of Laplace and wave equations in two dimensional Cartesian coordinates

Interior and exterior Dirichlet problems in polar coordinates

Separation of variables method for solving wave and diffusion equations in one space variable

Fourier series and Fourier transform

Laplace transform methods of solutions for the equations mentioned above