Math 319 > Downloads


Homework assignments Matlab files
  • 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
Mathematica files Lecture slides
  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

MATH 319: Introduction to Partial Differential Equations Winter 2011