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 L^{2} 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 R^{n} | ||
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) |