Math 425 - Notes and Homework
Thursday January 21, 2010
Topics for this week -
- Basic PDE concepts
- The "big three" (or four) PDEs - Laplace,
wave (and transport) equations.
- Methods for finding solutions - first-order equations like
3ux + 4uy = Q, where Q is zero, or
u, or u + f(x,y). Initial-value
- Initial, boundary and initial/boundary value problems for second
Second Homework Assignment - due Thursday, January 28
- Reading: Read the notes on vecctor fields/first-order
- Find the general solution of uxy =
x2y for the function
- Ditto for: yuxy + 2ux = x
(Hint: first integrate with respect to x)
- For the preceding PDE, find the solution that satisfies
u(x,1) = 0 and u(0,y) = 0.
- Solve: ux + 2uy = 0,
5ux + 6uy = 0,
cux + duy = 0.
(These are three separate problems)
- Solve the equation yux + xuy = 0
with u(0,y) = exp(-y2). In which region
the xy plane is the solution uniquely determined?
- Solve ux + uy + u =
ex+2y with u(x,0) = 0.
- Solve the equation ux + 2uy +
(2x - y)u = 2x2 + 3xy -