| week | date | reading | daily topics & demos | worksheets |
|---|---|---|---|---|
| 1 | Mar 28 W | website, 1.1 | Dimensional analysis | dimanal, solns |
| 29 Th X-hr | lin. algebra! | problem session on dimensional analysis | ||
| 30 F | 1.2 | Scaling | scaling (w/ solns) | |
| Apr 2 M | 1.3 | review ODE solution methods | ode1 | |
| 2 | 4 W | 1.4 | HW1 due. review 2D ODEs (phase plane), stability | phaseplane |
| 5 Th X-hr | Matlab links |
numerical solution and plots of ODEs with Matlab, intro46.m
| ||
| 6 F | 2.1.1-2 | Regular perturbation | regpert | |
| 9 M | 2.1.3-4 | Poincare-Linstedt method, asymptotic analysis, O(.) and o(.) | ||
| 3 | 11 W | 2.2 | HW2 due. Singular perturbation | dombal |
| 12 Th X-hr | - | |||
| 13 F | 2.3 | Boundary layers and uniform approximation | ||
| 16 M | 2.4 | Initial layers | ||
| 4 | 18 W | 2.5 | HW3 due. WKB approximation | wkb |
| 19 Th X-hr | - | |||
| 20 F | 2.6.1-2 | WKB eigenvalues, asymptotic expansion of integrals | wkbeig | |
| 23 M | 2.6.3 | Stationary phase integrals | ||
| 5 | 25 W | 4.1 | HW4 due.Asymptotic expansion by parts. | |
| 26 Th X-hr | - | practise problems (also this) | ||
| Midterm 1: Thursday April 26, 6-8 pm, Kemeny 008. (solutions) | ||||
| 27 F | 4.1 | Orthogonal expansions & Fourier series | ||
| 30 M | 4.1 | Uniform convergence, Bessel's inequality | bessel | |
| 6 | May 2 W | 4.2 | HW5 due. Sturm-Liouville problems. | |
| 3 Th X-hr | - | |||
| 4 F | 4.3.2 | Integral equations: Volterra equations | volterra | |
| 7 M | 4.3.3 | Degenerate Fredholm equations | ||
| 7 | 9 W | 4.3.4 | HW6 due. Symmetric Fredholm equations | |
| 10 Th X-hr | - | Review degenerate Fredholm | ||
| 11 F | 4.4 | Hilbert-Schmidt theorem, Green's functions | greens | |
| 14 M | 4.4 | Green's functions via eigenfunction expansion. Classifying PDEs. | ||
| 8 | 16 W | 6.1 | HW7 due. Integrating simple PDEs, fundamental solution, heat equation on R. | simple_pdes |
| 17 Th X-hr | - | practise problems and integral equation review | ||
| Midterm 2: Thursday May 17, 6-8 pm, Kemeny 008 (solutions) | ||||
| 18 F | 6.2.1-2 | Conservation laws, Green's identities, heat equation on Rn | ||
| 21 M | 6.2.3-5, 6.3 | Energy method for uniqueness, Laplace's equation, maximum principle. | ||
| 9 | 23 W | 6.4 | HW8 due. Eigenfunction (mode) expansions | separable |
| 24 Th X-hr | 6.5.2 | (replacing Monday lecture) The Fourier transform. | ||
| 25 F | 6.6 | Convolution and Fourier transform solution of PDEs. | conv | |
| 28 M | (no lecture: Memorial Day) | |||
| 10 | 30 W | - | HW9 due. Review (practise questions) | |
| Final Exam: Friday June 1, 8-11am, Kemeny 108 (solutions) | ||||