| Week 1 | ||
|---|---|---|
| Mon 25 Mar | 1.1: Dimensional Analysis |
Worksheet 1 solutions |
| Weds 27 Mar | 1.2: Scaling |
Worksheet 2 solutions |
| Thurs 28 Mar | Using Matlab to solve ODEs, Plus making
beautiful plots. Intro code Linear Algebra intro code |
|
| Fri 29 Mar | 1.3: Review ODE solution methods | Worksheet 3 solutions
Worksheet 4 solutions |
| Week 2 | ||
| Mon 1 Apr |
2.1.1-2: Regular perturbation of ODEs |
Worksheet 5 solutions |
| Weds 3 Apr |
2.1.3: Poincare-Linstedt method | |
| Thurs 4 Apr | 2.1.4: Asymptotic analysis, O(.) and o(.), pointwise vs
uniform convergence |
Worksheet 6 solutions |
| Fri 5 Apr |
2.2: Singular pertubation, dominant balancing | Worksheet 7 solutions |
| Week 3 | ||
| Mon 8 Apr |
2.3: Boundary layers and uniform approximation: real world examples | Inviscid Fluid
Vortex Shedding I Vortex Shedding II |
| Weds 10 Apr |
2.4: Initial layers | Worksheet 8 solutions |
| Thurs 11 Apr | 2.5: WKB approximation: non-oscillatory and oscillatory cases | Worksheet 9 solutions |
| Fri 12 Apr |
2.5.2: WKB eigenvalues 2007 Midterm 1 Solutions 2008 Midterm 1 Solutions 2011 Midterm 1 Solutions |
Worksheet
10 solutions |
| Week 4 | ||
| Mon 15 Apr |
Finish material + problem session | |
| Weds 17 Apr |
You get the day off |
|
| Fri 19 Apr |
4.1: Asymptotics of integrals. Orthogonal expansions and Fourier series | Fourier series code |
| Week 5 | ||
| Mon 22 Apr |
4.1 continued: Uniform vs L^2 convergence | Worksheet
11 solutions |
| 24 or 25 Apr |
Midterm 1, 5:00-7:00 pm You
can choose the date. |
Exam 1 solutions |
| Weds 24 Apr |
4.2: Bessel's inequality, Strum-Liouville problems | |
| Fri 26 Apr |
4.2: Strum-Liouville eigenvalue proofs | Worksheet
12 solutions |
| Week 6 | ||
| Mon 29 Apr |
4.3.1: Energy method and integral equations | |
| Weds 1 May |
4.3.2: Volterra equations, conversion to intial value problems,Picard's method | |
| Thurs 2 May | X-hr: practice converting Volterra equations to IVPs
and vise versa |
Worksheet 13 solutions |
| Fri 3 May |
4.3.3: Fredholm equations with degenerate kernels Some worked examples |
Worksheet
14 |
| Week 7 | ||
| Mon 6 May |
4.3.4: Symmetric Fredholm equations, Hilbert-Schmidt theorem | |
| Weds 8 May |
4.4.3: Application: Image-deblurring in 1D, convolution kernels, regularization Reference | Worksheet 15 solutions |
| Fri 10 May |
4.4.3,6.1: Green's functions, the eigenfunction expansion 2007 Midterm 2 Solutions 2008 Midterm 2 Solutions 2011 Midterm 2 Solutions |
Worksheet 16 solutions |
| Week 8 | ||
| Mon 13 May |
6.2.1-2: Conservation laws, multivariable notation, Green's identities, heat equation in R^n | Worksheet 17 solutions |
| Weds 15 May |
6.2.3-5: Energy method for uniqueness | Worksheet 18 solutions |
| Thurs 16 May |
Midterm 2, 5:00-7:00 pm Exam 2 solutions |
|
| Fri 17 May |
6.3: Laplace's and Poisson's equations, maximum principle | |
| Week 9 | ||
| Mon 20 May |
6.5.2: The Fourier transform | |
| Weds 22 May | 6.5.2: Convolution and Fourier transform solution of ODEs and PDEs Convolution applet | Worksheet 19 solutions |
| Thurs 23 May | X-hr: Using for the Fourier Transform backwards |
Fourier Transform table |
| Fri 24 May | No class |
|
| Week 10 | ||
| Mon 27 May | Memorial Day. No class | |
| Weds 29 May | Review/in class examples |
|
| Old Finals | Practice
questions 2007 Final solutions 2008 Final solutions 2009 Final solutions 2011 Final solutions |
|
| Fri 31 May | Final Exam, 3:00-6:00 pm, Location: Kemeny 006 | Final Exam solutions |
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