| week | date | reading | daily topics & demos | worksheets |
|---|---|---|---|---|
| 1 | Mar 26 W | website, 1.1 | Dimensional analysis | |
| 27 Th X-hr | lin. algebra! | problem session on dimensional analysis | dimanal_I, dimanal_II | |
| 28 F | 1.2 | Scaling | scaling (w/ solns) | |
| 31 M | 1.3 | review ODE solution methods | ode1 | |
| 2 | Apr 2 W | 2.1.1-2 | HW1 due. Regular perturbation | regpert |
| 3 Th X-hr | Matlab links |
numerical solution and plots of ODEs with Matlab, intro46.m.
Also consider Intro to Matlab workshop, 4-6pm.
| ||
| 4 F | 2.1.3 | Poincare-Linstedt method. | ||
| 7 M | 2.1.4 | asymptotic analysis, O(.) and o(.), pointwise vs uniform convergence. | ||
| 3 | 9 W | 2.2 | HW2 due. Singular perturbation, dominant balancing | dombal |
| 10 Th X-hr | - | |||
| 11 F | 2.3 | Boundary layers and uniform approximation (real world examples: bdry layer 1, 2, inviscid, shedding) | ||
| 14 M | 2.4 | Initial layers | initlayer | |
| 4 | 16 W | 2.5 | HW3 due. WKB approximation: non-oscillatory and oscillatory cases. | wkb |
| 17 Th X-hr | - | |||
| 18 F | 2.5.2 | WKB eigenvalues (plot, accuracy test code: wkb_acc, shooting) | wkbeig | |
| 21 M | 4.1 | Orthogonal expansions & Fourier series | ||
| 5 | 23 W | 4.1 | HW4 due. Uniform vs L2 convergence | L2conv |
| 24 Th X-hr | - | practise problems (also this) | ||
| Midterm 1 (solutions: Thursday April 24, 6-8 pm, Kemeny 105 (prac exam, solutions) | ||||
| 25 F | 4.2 | Bessel's inequality, Sturm-Liouville problems | bessel | |
| 28 M | 4.2 | Sturm-Liouville eigenvalue proofs | reality | |
| 6 | 30 W | 4.3.2 | HW5 due.Energy method. Integral equations: Volterra equations | volterra |
| May 1 Th X-hr | - | Volterra applications, Picard's method | ivpvolterra | |
| 2 F | 4.3.4 | Degenerate Fredholm equations degenerate Fredholm practise | ||
| 5 M | 4.3.4 | Symmetric Fredholm equations, Hilbert-Schmidt theorem. Worked examples for degenerate Fredholm | ||
| 7 | 7 W | - | HW6 due. Application: Image-deblurring in 1D, convolution kernels | deblur |
| 8 Th X-hr | - | |||
| 9 F | 4.4 | Deblurring, regularization, Green's functions. | greens | |
| 12 M | 4.4.3 | Greens functions, their eigenfunction expansion. | ||
| 8 | 14 W | 6.1 | HW7 due. Classifying PDEs, integrating simple PDEs, fundamental solution, heat equation on R. | simple_pdes |
| 15 Th X-hr | - | practise problems, integral equation review, practise midterm 2 (solutions). | ||
| Midterm 2: Thursday May 15, 6-8 pm, Kemeny 105 (solutions) | ||||
| 16 F | 6.2.1-2 | Conservation laws, multivariable notation, Green's identities, heat equation on Rn | ||
| 19 M | 6.2 | (no lecture; Alex away) | ||
| 9 | 21 W | 6.2.3-5, 6.3 | HW8 due Energy method for uniqueness, Laplace's and Poisson's equations, maximum principle. | greenident |
| 22 Th X-hr | 6.5.2 | (replacing Memorial day) The Fourier transform. | ||
| 23 Fr | 6.5.2 | Convolution and Fourier transform solution of ODEs and PDEs. applet | conv | |
| 26 M | (no lecture: Memorial Day) | |||
| 10 | 28 W | - | HW9 due. Review (practise questions, practise final, solutions) | |
| Final Exam: Saturday May 31, 8-11am, Haldeman 028 (solutions) | ||||