| Week 1 | ||
|---|---|---|
| Mon 24 Mar | 1.1: Dimensional Analysis Walter Lewin Pendulum Full Lecture |
Worksheet 1 Solutions |
| Weds 26 Mar | 1.2: Scaling |
Worksheet 2 Solutions |
| Thurs 27 Mar | Using Matlab to solve ODEs, Plus making
beautiful plots. Intro code Linear Algebra intro code |
|
| Fri 28 Mar | 1.3: Review ODE solution methods | Worksheet 3
Solutions |
| Week 2 | ||
| Mon 31 Mar |
2.1.1-2: Regular perturbation of ODEs |
Worksheet 4
Solutions Worksheet 5 Solutions |
| Weds 2 Apr |
2.1.3: Poincare-Linstedt method | |
| Thurs 3 Apr | 2.1.4: Asymptotic analysis, O(.) and o(.), pointwise vs
uniform convergence |
Worksheet 6 Solutions |
| Fri 4 Apr |
2.2: Singular pertubation, dominant balancing | Worksheet 7 Solutions |
| Week 3 | ||
| Mon 7 Apr |
2.3: Boundary layers and uniform approximation: real world examples | Inviscid Fluid
Vortex Shedding I Vortex Shedding II |
| Weds 9 Apr |
2.4: Initial layers | Worksheet 8 Solutions |
| Thurs 10 Apr | 2.5: WKB approximation: non-oscillatory and oscillatory cases | Worksheet 9 Solutions |
| Fri 11 Apr |
2.5.2: WKB eigenvalues 2007 Midterm 1 Solutions 2008 Midterm 1 Solutions 2011 Midterm 1 Solutions 2013 Midterm 1 Solutions |
Worksheet 10 Solutions |
| Week 4 | ||
| Mon 14 Apr |
4.1: Asymptotics of integrals. Orthogonal expansions and Fourier series | |
| Tues 15 Apr |
Midterm 1, 5:00-7:00pm Exam Solutions | |
| Weds 16 Apr |
4.1 continued: Uniform vs L^2 convergence | Worksheet 11 Solutions |
| Thurs 17 Apr |
4.2: Bessel's inequality, Strum-Liouville problems | |
| Fri 18 Apr |
4.2: Strum-Liouville eigenvalue proofs | Fourier
series code Worksheet 12 Solutions |
| Week 5 | ||
| Mon 21 Apr |
4.3.1: Energy method and integral equations | |
| Weds 23 Apr |
4.3.2: Volterra equations, conversion to intial value problems, Picard's method | |
| Thurs 1 May | X-hr: practice converting Volterra equations to IVPs
and vise versa |
Worksheet 13 Solutions |
| Fri 25 Apr |
4.3.3: Fredholm equations with degenerate kernels Some worked examples |
Worksheet
14 |
| Week 6 | ||
| Mon 28 Apr |
4.3.4: Symmetric Fredholm equations, Hilbert-Schmidt theorem | |
| Weds 30 Apr |
4.3.4: Symmetric Fredholm equations, Hilbert-Schmidt theorem (continued) | |
| Thurs 1 May |
4.4.3: Application: Image-deblurring in 1D, convolution
kernels, regularization Reference
2007 Midterm 2 Solutions 2008 Midterm 2 Solutions 2011 Midterm 2 Solutions 2013 Midterm 2 Solutions |
Worksheet 15 Solutions |
| Week 7 | ||
| Mon 5 May |
You get this week off. |
|
| Weds 7 May |
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| Fri 9 May |
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| Week 8 | ||
| Mon 12 May |
4.4.3,6.1: Green's functions, the eigenfunction expansion | Worksheet 16 Solutions |
| Tues 13 May |
Midterm 2, 5:00-7:00 pm Exam Solutions Problem 2 retake solution | |
| Weds 14 May |
6.2.1-2: Conservation laws, multivariable notation, Green's identities, heat equation in R^n | Worksheet 17 Solutions |
| Thurs 15 May |
6.2.3-5: Energy method for uniqueness | Worksheet 18 Solutions |
| Fri 16 May |
6.3: Laplace's and Poisson's equations, maximum principle | |
| Week 9 | ||
| Mon 19 May |
6.5.2: The Fourier transform | |
| Weds 21 May | 6.5.2: Convolution and Fourier transform solution of ODEs and PDEs Convolution applet 1 Convolution applet 2 | Worksheet 19 Solutions |
| Thurs 22 May | X-hr: Using for the Fourier Transform backwards Notes on how to use Table 6.2 backwards |
Fourier Transform table |
| Fri 23 May | No class |
|
| Week 10 | ||
| Mon 26 May | Memorial Day. No class | |
| Weds 28 May | Review/in class examples |
|
| Old Finals | Practice
questions 2007 Final solutions 2008 Final solutions 2009 Final solutions 2011 Final solutions 2013 Final solutions |
|
| Fri 30 May | Final Exam, 3:00-6:00 pm, Location: Kemeny 007 |
|
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