Fourier Series and Numerical Methods for PDEs

4-None

Introduces specific solution techniques used to solve the wave, heat and Laplace equations. Focuses on separation of variables, namely Fourier series, and a variety of numerical methods. Provides students with modern methods, harmonic analysis and numerical analysis, necessary to study and solve PDEs in a variety of applications. The fast Fourier transform is studied as well as finite difference methods for parabolic and elliptic PDEs and the finite element method for elliptic boundary value problems.