| week | date | reading | daily topics & demos | worksheets | |
|---|---|---|---|---|---|
| 1 | Mar 30 M | website, 1.1 | Dimensional analysis (& review linear algebra) | dimanal_I | |
| Apr 1 W | 1.2 | Scaling | scaling | ||
| 2 Th X-hr | linear algebra! | problem session on dimensional analysis | dimanal_II | ||
| 3 F | 1.3 | review ODE solution methods (Math 23) | ode1 | ||
| 2 | 6 M | 2.1.1-2 | Regular perturbation of ODEs | regpert | |
| 8 W | 2.1.3 | HW1 due. Poincare-Linstedt method. | |||
| 9 Th X-hr | Matlab links |
numerical solution and plots of ODEs with Matlab, intro46.m.
| |||
| 10 F | 2.1.4 | asymptotic analysis, O(.) and o(.), pointwise vs uniform convergence. | asympt | ||
| 3 | 13 M | 2.2 | Singular perturbation, dominant balancing | dombal | |
| 14 Tu | - | [if needed: 4-6pm Matlab intro session by Academic Computing, sign up] | |||
| 15 W | 2.3 | HW2 due. Boundary layers and uniform approximation (real world examples: bdry layer 1, 2, inviscid, shedding) | |||
| 16 Th X-hr | 2.4 | (moved from Friday) Initial layers | initlayer | ||
| 17 F | - | (no lecture; Alex away) | |||
| 4 | 20 M | 2.5 | WKB approximation: non-oscillatory and oscillatory cases. | wkb | |
| 22 W | 2.5.2 | HW3 due. WKB eigenvalues (plot, accuracy test code: wkb_acc, shooting) | wkbeig | ||
| 23 Th X-hr | - | ||||
| 24 F | 4.1 | Orthogonal expansions & Fourier series | |||
| 5 | 27 M | 4.1 | Uniform vs L2 convergence | L2conv | |
| 29 W | 4.2 | HW4 due. Bessel's inequality, Sturm-Liouville problems | bessel | ||
| 30 Th X-hr | - | practise problems, esp see practise exams linked on next line. | |||
| Midterm 1 (solutions): Thursday April 30, 6-8 pm, Kemeny 108 (prac exam, solutions), (prac exam, solutions) | |||||
| May 1 F | 4.2 | Sturm-Liouville eigenvalue proofs | reality | ||
| 6 | 4 M | 4.3.2 | (no lecture; Alex away) | ||
| 6 W | 4.3.4 | moved OH 4-5pm. Energy method. Integral equations | |||
| 7 Th X-hr | - | HW5 due. Volterra equations, conversion to IVPs. | volterra | ||
| 8 F | 4.3.4 | Volterra applications, second-order IVPs, Picard's method | ivpvolterra | ||
| 7 | 11 M | - | Degenerate Fredholm equations. Worked examples for degenerate Fredholm | ||
| 13 W | 4.4 | HW6 due. Symmetric Fredholm equations, Hilbert-Schmidt theorem. | |||
| 14 Th X-hr | - | Degenerate Fredholm practise, integral equation review. | degenerate | ||
| 15 F | 4.4.3 | Application: Image-deblurring in 1D (Tan pics), convolution kernels. Regularization, Green's functions. | deblur | ||
| 8 | 18 M | 4.4.3, 6.1 | Greens functions, their eigenfunction expansion. | greens | |
| 20 W | 6.2.1-2 | HW7 due. Conservation laws, multivariable notation, Green's identities, heat equation on Rn | |||
| 21 Th X-hr | - | practise problems, practise midterm 2 (solutions); practise midterm 2 (solutions). | |||
| Midterm 2: Thursday May 21, 6-8 pm, Kemeny 108 (solutions) | |||||
| 22 F | 6.2.3-5, 6.3 | Energy method for uniqueness, Laplace's and Poisson's equations, maximum principle. | greenident | ||
| 9 | 25 M | 6.2 | (no lecture: Memorial Day) | ||
| 27 W | 6.5.2 | HW8 due. The Fourier transform. | |||
| 28 Th X-hr | 6.5.2 | (replacing Memorial day) Convolution and Fourier transform solution of ODEs and PDEs. applet | conv | ||
| 29 Fr | p.391-394 | How to use Table 6.2 in reverse. | |||
| 10 | Jun 1 M | - | HW9 due. Review. practise questions, practise final (solutions), practise final (solutions). | ||
| Final Exam: Friday June 5, 11:30am-2:30pm, Kemeny 108 (solutions) | |||||