Partial Differential Equations

Polar coordinates, wave equation, Bessel's equation, Bessel's functions, waves on a disk.

Analysis, uniform convergence, Dirichlet Test for Uniform Convergence

Laplace's equation in rectangular coordinates in 2-dimensions, Poisson's equation, the Helmholtz equation, eigenvalues and eigenvectors, the Maximum Principle

2D Wave and Heat Equations in Rectangular Coordinates

d'Alembert solution, the Heat Equation. Dirichlet, Neumann, and Robin boundary conditions.

Fourier Series, Bessel's Inequality, Parseval's Inequality, Complex Fourier Series, Pointwise Convergence, Convergence Almost Everywhere, Convergence in the Mean, L1, L2, Hilbert Space.

Elements of Fourier Series, Gibbs Phenomenon, Gram-Schmidt Process, projections, inner products.

An introduction to partial differential equations. The Continuity Equations, Maxwell's Laws, The Wave Equation.