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## Syllabus

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
End of material covered by midterm 1

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
End of material covered by midterm 2

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

Fri 9 May

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