| Date |
Reading | Topics |
Written
Homework |
| 3/30 Mon | 1.1, 1.2 |
Dimensional analysis and scaling |
|
| 3/31 Tue, x-hour | |||
| 4/1 Wed |
1.2 |
Dimensional analysis and scaling | HW 1 (Solution) |
| 4/3 Fri | 1.3 |
Review of ODEs |
|
| 4/6 Mon | 3.1.1-3.1.2 |
Regular perturbation |
|
| 4/7 Tue, x-hour | |||
| 4/8 Wed | 3.1.3 |
The Poincare-Lindstedt Method |
HW 2 (Solution) |
| 4/10 Fri | 3.1.4 |
Asymptotic analysis |
|
| 4/13 Mon | 3.2 |
Singular perturbation |
|
| 4/14 Tue, x-hour | 3.3 |
Boundary layers and uniform approximations | |
| 4/15 Wed | 3.4 | Initial layers | HW 3 (Solution) |
| 4/17 Fri | No class |
||
| 4/20 Mon | No class |
||
| 4/21 Tue, x-hour | |||
| 4/22 Wed | 3.5 |
The WKB approximation and
Review |
HW 4 (Solution) |
| 4/24 Fri | Midterm
1 (4:00-6:00pm, Location : Kemeny 108) |
Midterm
Solution |
|
| 4/24 Fri | 3.5, 3.6 | The WKB approximation, Asymptotic expansion of integrals | |
| 4/27 Mon | 5.1-5.2 |
Boundary value problem, Sturm-Liouville problems |
|
| 4/28 Tue, x-hour | |||
| 4/29 Wed | 5.2 |
Sturm-Liouville problems | HW 5 (Solution) |
| 5/1 Fri | 5.2-5.3 |
Sturm-Liouville problems | |
| 5/4 Mon | 5.2-5.3 |
Orthogonal functions |
|
| 5/6 Wed | 5.3 | Fourier Series |
HW 6 (Solution) |
| 5/7 Thur, x-hour | |||
| 5/8 Fri | 5.3 |
Fourier Series |
|
| 5/11 Mon | 5.4.1 |
Integral Equations, Volterra Equations |
|
| 5/13 Wed | 5.4.1 |
Volterra Equations, Review | HW 7 (Solution) |
| 5/14 Thur, x-hour | |||
| 5/14 Thur | Midterm 2 (4:00pm-6:00pm, Location : Kemeny 108) | Midterm Solution | |
| 5/15 Fri | 5.4.2 | Fredholm equations with Degenerate Kernels |
|
| 5/18 Mon | 5.4.2 | Fredholm equations with Degenerate Kernels | |
| 5/19 Tue, x-hour | |||
| 5/20 Wed | 5.4.3 | Fredholm equations with Symmetric Kernels | HW 8 (Solution) |
| 5/22 Fri | 5.5 |
Green's function | |
| 5/25 Mon | Memorial day (no class) |
||
| 5/26 Tue, x-hour | 5.5 | Green's function via eigenfunctions | |
| 5/27 Wed | 6.2.3-6.2.3 | Conservation laws, Several dimensions, Green's identities | HW 9 (Solution) (Will not be collected) |
| 5/29 Fri | 6.2.5 | Energy method for uniqueness | |
| 6/1 Mon | 6.3.1-6.3.2 |
Laplace and Poission equation, Separation of variables | |
| 6/3
Wed |
Final exam (3:00pm-6:00pm, Location : TBA) |