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 
2.1.12: Regular perturbation of ODEs 
Worksheet 4
Solutions Worksheet 5 Solutions 
Weds 2 Apr 
2.1.3: PoincareLinstedt 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: nonoscillatory 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, 5:007:00pm Exam Solutions  
Weds 16 Apr 
4.1 continued: Uniform vs L^2 convergence  Worksheet 11 Solutions 
Thurs 17 Apr 
4.2: Bessel's inequality, StrumLiouville problems  
Fri 18 Apr 
4.2: StrumLiouville 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  Xhr: 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, HilbertSchmidt theorem  
Weds 30 Apr 
4.3.4: Symmetric Fredholm equations, HilbertSchmidt theorem (continued)  
Thurs 1 May 
4.4.3: Application: Imagedeblurring 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 


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, 5:007:00 pm Exam Solutions Problem 2 retake solution  
Weds 14 May 
6.2.12: Conservation laws, multivariable notation, Green's identities, heat equation in R^n  Worksheet 17 Solutions 
Thurs 15 May 
6.2.35: 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  Xhr: 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, 3:006:00 pm, Location: Kemeny 007 
