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## Syllabus

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
End of material covered by midterm 1

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
End of material covered by midterm 2

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