- Assignment 1. Due Thursday, January 27. Solutions to Problems 3, 5, and 9.
- Assignment 2. Due Thursday, February 17
- Midterm exam. Due Thursday, March 10
- Assignment 3. Due Thursday, March 24
- Assignment 4. Due Thursday, April 7
- Solutions to selected problems from Assignments 3 and 4.

- sqgrid.m - Generates a mesh on a square
- lapdir.m - 5-point matrix for the Dirichlet problem for the Poisson equation
- square.m - An example driver file that uses the preceding two functions
- bump.m - Tent function to be used as an initial condition
- advection.m - First order finite difference solver for the advection equation
- widebump.m - Wider tent function to be used as an initial condition
- widebump1.m - Tilted tent function to be used as an initial condition
- heat.m - Explicit finite difference solver for the heat equation
- heatimp.m - Implicit finite difference solver for the heat equation
- smoothbump.m - Smoother bump function suitable for wave.m
- wave.m - Finite difference solver for the wave equation

- graphs10.nb - graphics of Lecture 10
- graphs11.nb - graphics of Lecture 11
- graphs15.nb - graphics of Lecture 15
- graphs19.nb - graphics of Lecture 19
- graphs20.nb - graphics of Lecture 20
- graphs21.nb - graphics of Lecture 21
- graphs27.nb - graphics of Lecture 27
- graphs30.nb - graphics of Lectures 28-30

- Basic concepts
- Linear algebra and simple ODEs
- Initial and boundary value problems in 1 dimension
- Poisson equations. Introduction to electrostatics
- Poisson equations in 3D
- Dirichlet problem
- Finite difference method
- Dirichlet- and maximum principles
- Advection in 1D
- Wave equation in 1D
- D'Alambert's solution
- Method of characteristics and the CFL condition
- Waves in space and on the plane
- Spherical waves, energy inequality, and uniqueness
- Heat equation on the real line
- Convection diffusion, steady state, and explicit finite differences
- Implicit finite differences, classification of second order PDE
- Crash course on Matlab
- Fourier sine series
- Fourier sine series (continued)
- Introducing separation of variables
- General discussion on PDE theory, ill-posedness
- Separation of variables for heat and wave
- Neumann boundary conditions and Fourier cosine series
- Problems on the circle, Fourier series, and inhomogeneous boundary conditions
- Inhomogeneous equations, reaction and damping terms
- Rectangular problems
- Harmonic functions on the disk and the Poisson kernel
- Laplace eigenproblem on the disk and the Bessel functions
- Bessel functions and the Laplace eigenfunctions on the disk
- Problems on the disk
- Examples in separation of variables