Required Text: James P. Keener, Principles of Applied Mathematics: Transformation and Approximation, Perseus Books, Reading, Massachusetts, 1995.
Topics Covered and Approximate Schedule
| Week 1 | Calculus of Variations - 5.1.5, 5.2, & sufficient conditions for an extremum |
|---|---|
| Week 2 | Sufficient conditions for an extremum, 5.3, 5.4 |
| Week 3 | Complex variables - 6.1, 6.2 |
| Week 4 | 6.4, 6.5 |
| Week 5 | 6.5, 6.3 |
| Week 6 | Fourier transforms - notes, 7.2 |
| Week 7 | Fourier transforms - continued |
| Week 8 | Finish FT; review; Test 1 (Friday, 3/10/06) |
| Week 9 | Other transforms - 7.3, 7.4 |
| Week 10 | FT of distributions, Sobolev spaces |
| Week 11 | Wave equation - 8.2 |
| Week 12 | Asymptotic expansions - 10.1, 10.2, 10.3 |
| Week 13 | 10.3, 10.4, 10.5 |
| Week 14 | 10.5; Regular perturbation theory - 11.1, 11.2 |
| Week 15 | 11.3; review |