MATH 3160

This course begins with an introduction to Fourier series and Fourier transforms. Next, series solutions of ordinary differential equations are examined. Power series methods are applied to obtain solutions near ordinary points and regular singular points. Students then consider Sturm-Liouville boundary value problems and series of eigenfunctions. Initial value and boundary value problems involving partial differential equations are then examined. Solutions are found using the methods of separation of variables, Green's functions and integral transforms. Physical applications discussed include the heat/diffusion equation, wave equation and Laplace's equation.