Math 412 Homework -- Fall 2001
Assignment 1.
- Read sections 1.1-1.4, 2.1-2.3 in Haberman.
- Do exercises 1.2.1, 1.3.2, 1.4.1(a,c,f), 2.3.1(a,b,d), 2.3.2(d),
2.3.3(a,c).
Due Thursday, 9/6/01.
Assignment 2.
- Read sections 2.4.2, 2.5.2, 2.5.4, 3.1-3.3.
- Do exercises 1.4.3, 1.5.3, 2.3.6, 2.4.2.
- Solve the problem of heat flow in a ring (see § 2.4.2), given
that the initial temperature is
where T is a constant.
Due Thursday, 9/13/01.
Assignment 3.
- Read sections 3.3-3.5.
- Do exercises 2.5.3(a), 2.5.6(b), 2.5.8(a,b), 2.5.10,
3.2.1(c,e,f), 3.2.2(b,f).
- Use the maximum and minimum principles for Laplace's equation
(see § 2.5.4) to show that the maximum of the absolute value of
the steady state temperature occurs on the boundary.
Due Thursday, 9/20/01.
Assignment 4.
- Read sections 3.6, 10.1-10.3.
- Do exercises 3.3.1(b,d), 3.3.2(a,d), 3.3.3(b), 3.3.15, 3.3.18.
(Hint: in 3.3.18, look at the appropriate periodic extension for each
case.)
Due Thursday, 9/27/01.
Assignment 5.
- Read sections 10.4, 10.6.1, 10.6.3.
- Do exercises 10.3.1(a), 10.3.3, 10.3.6, 10.3.7, 10.3.13.
Due Friday, 10/12/01.
Assignment 6.
- Read sections 10.6.3, 12.1-12.3.
- Do exercises 10.3.14(a,b,c), 10.4.3(a), 10.4.5, 10.6.18.
- Follow the steps below to find the Fourier transform of a Gaussian,
g(x) = exp(-a x2).
Due Thursday, 10/18/01.
Assignment 7.
- Read sections 5.1-5.6.
- Do exercises 12.2.2, 12.2.3, 12.2.5(a), 12.3.1, 12.3.3, 12.3.5,
12.3.6.
Due Thursday, 10/25/01.
Assignment 8.
- Read sections 5.5-5.8.
- Do exercises 5.3.3, 5.3.8, 5.3.10(a,b,c,d,e) (We did 5.3.9 in
class on 10/25), 5.4.2, 5.4.3.
Due Thursday, 11/1/01.
Assignment 9.
- Read sections 5.8, 5.10, 7.1, 7.2, 7.4, 7.7.
- Do exercises 5.5.1(a,c,f,g), 5.5.3 (Note: this is not
necessarily a Sturm-Liouville operator), 5.5.7, 5.6.1(a,c), 5.6.2
Due Thursday, 11/8/01.
Assignment 10.
- Read sections 7.7, 7.8, 7.10.
- Do exercises 5.8.6, 5.8.8(a,c), 5.10.2(b), 5.10.4(a), 5.10.6,
7.3.4(b).
Due Tuesday, 11/20/01.
Assignment 11.
- Read sections 7.8, 7.10.
- Do exercises 7.7.1, 7.7.3, 7.7.6(b), 7.7.10, 7.7.12(d,e).
Due Tuesday, 11/29/01.