Math 412-200 Summer II, 2011
Assignments
Assignment 1.
- Read sections 1.1-1.5, 2.1-2.3, 2.4.2.
- Do exercises 1.2.3, 1.3.2, 1.4.1(f), 1.4.3, 2.3.1(a,b),
2.3.2(d,e), 2.3.3(a,b), 2.3.6, 2.4.2 [Hint: Separete variables and
use your solution to 2.3.2(e).]
Due Tuesday, 7/9/11.
Assignment 2.
- Read sections 2.5, 3.1-3.3.
- Do exercises 2.4.1 (see §2.4.1), 2.5.3(a), 2.5.5(a),
2.5.8(a,b), 2.5.10, 2.5.19, 3.2.1(c,e,f), 3.2.2(b,f).
- 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 Friday, 7/15/11.
Assignment 3.
- Read sections 3.4, 3.5, 4.4, 12.3
- Do exercises 3.3.1(b,d), 3.3.2(a,d), 3.3.5(a), 3.3.15, 3.3.18.
(Hint: in 3.3.18, look at the appropriate periodic extension for each
case.), 3.4.5, 3.5.2, 3.5.7
- Differentiate the cosine series obtained in 3.3.5(a) to find the
sine series for f(x) = x, where 0 ≤ x ≤ L.
- Integrate the cosine series in 3.3.5(a) to find the sine series
for x3 − L2x.
Due Wednesday, 7/20/11.
Assignment 4.
- Read sections 5.1-5.5
- Do exercises 4.4.3(b), 4.4.8, 4.4.9, 4.4.10(a,b), 4.4.13(a),
12.3.1, 12.3.5, 5.3.4(a,b), 5.3.5, 5.3.8, 5.3.10(a,b,c,d,e).
Due Tuesday, 7/26/11.
Assignment 5.
- Read sections 5.6-5.8, 5.10, 7.1-7.3
- Do exercises 5.4.2, 5.5.1(a,c), 5.5.3, 5.6.1(b), 5.7.2, 5.8.3,
5.8.8(a,b,c), 5.10.2(b), 5.10.4(a).
- For each of the Sturm-Liouville problems below, show, by
integrating by parts, that the eigenfunctions corresponding to
distinct eigenvalues are orthogonal.
- p(x) = (x2+1)−1, σ = 2, q(x) =
−x; φ(0) = 0 and φ(1) = 0.
- p(x) = 1, σ = x; q = 0; φ(0) = 0 and φ(2) +
φ′(2) = 0.
- p(x) = 1, σ = 1; q = 0; φ(0) = φ(1) and
φ′(0) = φ′(1).
Due Monday, 8/1/11.
Assignment 6.
- Read sectionns 7.7, 7.8
- Do exercises 7.7.1, 7.7.2(d), 7.7.3(a), 7.7.7, 7.7.11, 7.12(d,e)
Due Friday, 8/5/11.
Assignment 7.
- Read sectionns 10.1-10.3, 10.4.2, 10.4.3
- Do exercises 10.3.1, 10.3.5, 10.3.7, 10.3.8, 10.4.3(a)
Due Monday, 8/8/11.