Partial Differential Equations, Spring 2018

Mon 5/14: Office hours and final exam.

Mon 5/7: Solution to Wave equation in 2d and 3d; Huygens’s principle.

Thu 5/3: Causality for wave equation in 3D.

Tue 5/1: No office hours on 5/1.

Mon 4/30: Solid vibrations in a ball; spherical harmonics.

Thu 4/26: Wave and Heat equations on domains; vibrations of a drum.

Mon 4/23: Bacc week: no class.

Mon 4/16: General eigenvalue problems for the Laplacian.

Thu 4/12: Green’s Functions.

Mon 4/9: Green’s Functions.

Thu 4/5: Greens Identities.

Mon 4/2: Poisson Kernel.

Thu 3/29: Solving Laplace’s Equation by separation.

Mon 3/26: Harmonic functions and the Laplacian.

Thu 3/15: Convergence of Fourier Series.

Thu 3/8: Review for Midterm.

Mon 3/5: Fourier series continued: even/odd/periodic extensions, general orthogonality.

Thu 3/1: Fourier Series.

Mon 2/26: Separation of variables for Dirichlet and Neumann problems in 1+1D.

Thu 2/22: Diffusions and waves with a source.

Mon 2/19: Diffusion on the half line.

Thu 2/15: Diffusion on the whole line.

Mon 2/12: Uniqueness, stability for the diffusion equation.

Thu 2/8: Wave equation in 1+1D.

Mon 2/5: Physical derivation of diffusion equation; initial and boundary value problems.

Thu 2/1: First order linear PDE, continued; Physical derivations.

Mon 1/29: What is a PDE; First order linear PDE.