Instructor: Thomas W. Carr
Assignment | Description | Section | Problems |
Due Date |
1 |
Boundary Conditions |
1.3 |
1.3.2 |
Tues., Sept. 3 |
- |
Equilibrium |
1.4 |
1.4.1f & g, 1.4.3 |
- |
Two & Three Dimensions |
1.5 |
1.5.5, 1.5.9a |
2 |
Linearity, Superposition |
2.2 |
2.2.3 |
Tues., Sept. 10 |
- |
Separation |
2.3 |
2.3.1a & b |
- |
Boundary Value Problems |
2.3 |
2.3.2e & f |
3 |
Heat Equ. & Separation |
2.3 |
2.3.3b,
2.3.7
page1,
page2 |
Tues., Sept. 17 |
- |
Separation (cont.) |
2.4 |
2.4.1b, 2.4.2 |
pssst.... |
4 |
Laplace Equ. & Separation |
2.5 |
2.5.1a,
2.5.6a,
2.5.15a |
Tuesday, Sept. 24 pssst.... |
Exam 1 |
Heat, Laplace & Separation |
Chap 1 & 2 |
All of them |
Thursday, Sept 26 |
5 |
Fourier Series |
3.3 |
3.3.1e, 3.3.3b |
Tuesday, Oct. 8 pssst.... |
- |
Eigenfunction Expansions |
3.4 |
3.4.9, 3.4.12 |
- |
Vibrating String Derivation |
4.3 |
4.3.2 |
7 |
Vibrating String w/ Fixed Ends |
4.4 |
4.4.3, 4.4.5 |
Thursday, Oct. 17 |
- |
Sturm-Liouville Intro |
5.3 & 5.4 |
5.3.3, 5.3.7, 5.4.5 |
pssst.... |
8 |
Sturm-Liouville Properties |
5.5 |
5.5.1c, 5.5.2,
5.5.11 |
Tuesday, Oct. 22 |
9 |
S.L. & BC's of 3rd kind |
5.8 |
5.8.5 page1
page2 |
Tuesday, Oct. 29 |
Exam 2 |
Fourier, Strings and Sturm-Liouville |
Chap 3,4 & 5 |
All of them |
Thursday, Oct. 31 |
10 |
Heat Equ. in 2D-space |
7.3 |
7.3.3 |
Tuesday, Nov. 12 |
11 |
Higher-D eigenvalue problems |
7.5> |
7.5.1, 7.5.2 (7.6.1) |
Tuesday, Nov. 12 |
12 |
Circular Domains |
7.7 |
7.7.3,
7.7.7, 7.7.10 |
Tuesday, Nov. 19 pssst.... |
13 |
Prop. of Fourier Trans. |
10.3 |
10.3.5, 10.3.6, 10.3.11 |
Tuesday, Nov. 26 |
- |
Fourier Trans. & Heat Equ. |
10.4 |
10.4.3, 10.4.4 |
14 |
More Fourier Transforms |
10.6 |
10.6.1(b), 10.6.10, 10.6.11(c), 10.6.13 |
|
Assignment | Description | Section | Problems | Due Date |
1 |
Eigenfunction Expansions |
8.3 & 8.4 |
8.3.1(f,g),
8.4.2 |
Thu, 1/30 |
|
Green's Functions |
9.3 |
9.3.1 |
|
2 |
Green's Functions |
9.3 |
9.3.6(a,b),
9.3.9,
9.3.12(a,b),
9.3.13 pssst.... |
Thu, 2/6 |
3 |
Adjoint Operator |
5.5 |
5.5.11 (see above for solutions) pssst.... |
Tue, 2/18 |
|
Modified Green's F. |
9.4 |
9.4.2-I,
9.4.2-II,
9.4.2-III,
9.4.7-I,
9.4.7-II
|
|
|
Exam 1 |
|
page1,
page2,
page3,
page4 |
Thu, Feb 20 |
4 |
G.F. for Poisson's Equ. |
9.5 |
9.5.5, 9.5.7
9.5.9(b),
9.5.10(a,b),
9.5.13 pssst....
|
Thu, Mar 6 |
5 |
G.F. for Wave Equation. |
11.2 |
11.2.4,
11.2.6,
11.2.7a,
11.2.7b,
11.2.10
|
Tue, Mar 25 |
6 |
G.F. for Heat Equation. |
11.3 |
11.3.2c, 11.3.3
|
Tue, Apr 1 |
|
Exam 2 |
|
solutions |
Thu, April 3 |
7 |
Characteristics (1-dir) |
12.2 |
12.2.1, 12.2.4,
12.2.5d
|
Thu, April 10 |
8 |
Boundary reflections |
12.4 |
12.4.6
|
Tue, April 22 |
|
Quasilinear PDE |
12.6 |
12.6.4, 12.6.7a, 12.6.9a,
12.6.6a,
12.6.19(a,b)
|
9 |
Dispersion |
14.2 |
14.2.1(b,c), 14.2.5, 14.2.9(c) |
Thu, May 8 |
|
M. of Stationary Phase |
14.5 |
14.5.2, 14.5.3 |
|
10 |
Slowly Varying Waves |
14.6 |
14.6.3 |
- |
|
Envelope Equations |
14.7 |
14.7.3(b) |
|
Exam 3 |
|
|
Thu, May 1 |