Math 333 Class Page

Course syllabus
Course calendar
Homework assignments
Lecture notes
KnightVision (use for getting HW/exam solutions)
Grading Codes
Lecture notes on the finite element method
Professor Scofield's homepage

General: Octave diary, containing commands demonstrated in class Sept. 25
An ODE (BVP): Octave program from Sept. 23 class for solving BVP: y″ + y = 0, y(0) = y(π) = 0
1st-order PDEs:

MATHEMATICA notebook solving u_t + 3x^2/3 u_x = 0, u(0, x) = sin x via characteristics
Octave programs from Sept. 23 for solving transport equation via centered and backward difference approximations to the spatial derivative

2nd-order PDEs:

Finite differences for Poisson problems in a rectangle of the plane:

main program: poissonSolver.m
files that encode the specifics for various problems

psset1.m : Laplace's equation on 0 < x, y < 1, zero Dirichlet BCs except u(x, 0) = x³(1 - x)
psset2.m : Laplace's equation on 0 < x < 0.5, 0 < y < 1, BCs u(0, y) = 4y, u(0.5, y) = 4, u(x, 0) = 16x², u(x, 1) = 4
psset3.m : Laplace's equation on 0 < x, y < 1, zero Dirichlet BCs except along y = 0, which is “hat”-shaped
psset4.m : Poisson's equation -Δu = [(3x + x²) y (1 - y) + (3y + y²) x (1 - x)] e^x+y on 0 < x, y < 1, zero Dirichlet BCs

Finite differences schemes for one-dimensional heat equation:

explicit algorithm

main program: fdHeatSolver.m
file heatSet1.m: with specifics for u_t = u_xx on 0 < x < 1, t > 0, zero Dirichlet BCs, IC as in Olver, p. 123, Equation (4.25)

implicit algorithm

main program: implicitFDHeatSolver.m
file impHeatSet1.m: with specifics for same heat problem as above

Finite Element Method

file stanoP436.m: uses hat-function basis to solve ODE/BVP -y″ = f (x), subject to y(0) = 0 = y(1), with
f (x) = 100 sin(sign(x - .5) exp(1/(4|x - .5|^1.05 + .3))) exp(1/(4|x - .5|^1.2 + .2) - 100(x - .5)²).

“A simple proof that the world is three-dimensional”, by Tom Morley (1985)

Original article, from SIAM Review (Use JSTOR link), vol. 27, no. 1, pp. 69-71.
For errata, follow this same link, but select vol. 28, no. 2, p. 229 (1986).

Can one hear the shape of a drum?

Wikipedia entry on this subject
A student project, providing a brief history of the problem
Original article of this title, by Mark Kac (1966), American Mathematical Monthly, 73 (4, part 2): 1-23.

OCTAVE, a free MATLAB clone | a tutorial | online documentation
Mozilla's homepage, from which you can download Firefox browser
Online Mathematica integrator

Math 333A Partial Differential Equations Fall, 2009

Math 333A
Partial Differential Equations
Fall, 2009