AMATH 403/503 - Homework 1

Due: Wednesday, April 8

Problems for both 403 & 503 (from Haberman):

1. exercise 1.2.4 (b)

2. exercise 2.3.3 (a),(b),(d)

3. exercise 2.3.4 (b)

4. exercise 2.3.7

Problems for 503 only:

5. Consider the following PDE (and assume k > 0):

ut = kuxxu(0, t) = 0

u(1, t) = 0

u(x, 0) = sin(pix)

Attempt a solution using separation of variables. Explain why the method fails (hint: consider the convergence of theseries).

6. Solve the following PDE using separation of variables.

ut = kuxx

u(0, t) = 1

ux(1, t) = 0

u(x, 0) = 0

Describe, using physical intuition, what this solution should do as t. Does your solution show the same behavior?

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