Linear Analysis
Math 309 serves as the culmination of the Math 307-8-9 program in linear analysis. It combines analysis tools and ideas (such as series expansions, complex numbers and exponentials, and differential equations) from Math 307 with comparabale content (eigenvalues, and difference equations, orthogonal bases, projections and best approximations) from Math 308. These tools are applied to the solution and qualitative study of linear systems of ordinary differential equations, and to the analysis of classical partial differential equations (heat, wave, Laplace). In the case of partial differential equations, separation of variables is used to obtain boundary value problems which are then solved and are used to generate the Fourier series solutions of the original partial differential equation.