Downloads

• 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

1. Basic concepts
2. Linear algebra and simple ODEs
3. Initial and boundary value problems in 1 dimension
4. Poisson equations. Introduction to electrostatics
5. Poisson equations in 3D
6. Dirichlet problem
7. Finite difference method
8. Dirichlet- and maximum principles
9. Advection in 1D
10. Wave equation in 1D
11. D'Alambert's solution
12. Method of characteristics and the CFL condition
13. Waves in space and on the plane
14. Spherical waves, energy inequality, and uniqueness
15. Heat equation on the real line
16. Convection diffusion, steady state, and explicit finite differences
17. Implicit finite differences, classification of second order PDE
18. Crash course on Matlab
19. Fourier sine series
20. Fourier sine series (continued)
21. Introducing separation of variables
22. General discussion on PDE theory, ill-posedness
23. Separation of variables for heat and wave
24. Neumann boundary conditions and Fourier cosine series
25. Problems on the circle, Fourier series, and inhomogeneous boundary conditions
26. Inhomogeneous equations, reaction and damping terms
27. Rectangular problems
28. Harmonic functions on the disk and the Poisson kernel
29. Laplace eigenproblem on the disk and the Bessel functions
30. Bessel functions and the Laplace eigenfunctions on the disk
31. Problems on the disk
32. Examples in separation of variables