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Last update:
May 06. 2011 11:40:11
Math 319
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Homework assignments
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.
Matlab files
sqgrid.m
 Generates a mesh on a square
lapdir.m
 5point 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
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 2830
Lecture slides
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, illposedness
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
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MATH 319: Introduction to Partial Differential Equations Winter 2011
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