week | date | reading | daily topics & demos | worksheets | |
---|---|---|---|---|---|
1 | Mar 28 M | website, 1.1 | Dimensional analysis (& review linear algebra Math 22/24) | dimanal_I | |
30 W | 1.2 | Scaling | scaling | ||
31 Th X-hr | linear algebra! | problem session on dimensional analysis | dimanal_II | ||
Apr 1 F | 1.3 | review ODE solution methods (Math 23) | ode1 | ||
2 | 4 M | 2.1.1-2 | Regular perturbation of ODEs | regpert | |
6 W | 2.1.3 | HW1 due. Poincaré - Linstedt method. | |||
8 Th | - | (no X-hr) | |||
9 F | Matlab links | Guest lecture
(Katie Kinnaird):
install Matlab ahead of time. solving ODEs and plotting solutions. Use intro46.m .
| |||
3 | 10 M | 2.1.4 | Asymptotic analysis, O(.) and o(.), pointwise vs uniform convergence. | asympt | |
12 W | 2.2 | HW2 due. Singular perturbation, dominant balancing | dombal | ||
13 Th X-hr | 2.4 | (make-up lecture) Boundary layers and uniform approximation; real world examples: bdry layer 1, 2, inviscid, shedding | |||
14 F | 2.3 | Initial layers | initlayer | ||
4 | 18 M | 2.5 | WKB approximation: non-oscillatory and oscillatory cases. | wkb | |
20 W | 2.5.2 | HW3 due. WKB eigenvalues (plot, accuracy test code: wkb_acc, shooting) | wkbeig | ||
21 Th X-hr | - | ||||
22 F | 4.1 | Asymptotics of integrals. Orthogonal expansions & Fourier series | |||
5 | 25 M | 4.1 | Uniform vs L^{2} convergence | L2conv | |
27 W | 4.2 | HW4 due. Bessel's inequality, Sturm-Liouville problems | bessel | ||
28 Th X-hr | - | practise problems, esp. see practise exams linked on next line. | |||
Midterm 1 (solutions): Thursday April 28, 6-8 pm, Carson 60 (07 prac mid1, solutions), (08 prac mid1, solutions), (09 prac mid1, solutions) | |||||
29 F | 4.2 | Sturm-Liouville eigenvalue proofs | reality | ||
6 | May 2 M | 4.3.2 | Energy method. Integral equations | ||
4 W | 4.3.4 | HW5 due. Volterra equations, conversion to IVPs. | volterra | ||
5 Th X-hr | - | ||||
6 F | 4.3.4 | Volterra applications, second-order IVPs, Picard's method | ivpvolterra | ||
7 | 9 M | - | Degenerate Fredholm equations. Worked examples for degenerate Fredholm | ||
11 W | 4.4 | HW6 due. Symmetric Fredholm equations, Hilbert-Schmidt theorem. | |||
12 Th X-hr | - | Degenerate Fredholm practise, integral equation review. | degenerate | ||
13 F | 4.4.3 | Application: Image-deblurring in 1D (Tan pics), convolution kernels, regularization. | deblur | ||
8 | 16 M | 4.4.3, 6.1 | Green's functions, their eigenfunction expansion. | greens | |
18 W | 6.2.1-2 | HW7 due. Conservation laws, multivariable notation, Green's identities, heat equation on R^{n} | simple_pdes | ||
19 Th X-hr | - | practise problems, and practise exams linked on the next line. | |||
Midterm 2 (solutions): Thursday May 19, 6-8 pm, Carson 60 (07 prac mid2, solutions), (08 prac mid2, solutions), (09 prac mid2, solutions) | |||||
20 F | 6.2.3-5, 6.3 | Energy method for uniqueness, Laplace's and Poisson's equations, maximum principle. | greenident | ||
9 | 23 M | 6.5.2 | The Fourier transform. | ||
25 W | 6.5.2 | HW8 due. Convolution and Fourier transform solution of ODEs and PDEs. applet | conv | ||
27 Fr | p.391-394 | How to use Table 6.2 in reverse. | |||
10 | 30 M | - | (no lecture: Memorial Day) | ||
June 1 W | - | HW9 due. Review. practise questions; 07 prac final (solutions), 08 prac final (solutions), 09 prac final (solutions). | |||
Final Exam (solutions): Friday June 3, 3-6pm, Kemeny 007. |