Day  Topics  Notes 
09Jan  Section 1.1: finite dimensional vector spaces  
11Jan 
Section 1.2: Spectral theory for matrices Section 1.3: Geometrical significance of eigenvalues 

18Jan 
Section 1.4: Fredholm Alternative Section 1.5: Least Squares SolutionsPseudo Inverses 

23Jan 
Section 1.5: Singular value decomposition Section 1.6: Applications of eigenvectors and values 

25Jan 
Section 2.1: Complete vector spaces Section 2.2: Approximation in Hilbert spaces 

30Jan  Section 2.2: Approximation in Hilbert spaces: Fourier series and Orthogonal Polynomials  
1Feb  Section 2.2: Approximation in Hilbert spaces: Discrete Fourier Series and the FFT  
6Feb  Section 2.2: Approximation in Hilbert spaces: Wavelets  
8Feb  Section 2.2: Approximation in Hilbert spaces: Multiresolution analysis and Finite Elements  
13Feb 
Section 2.2: Approximation in Hilbert spaces: Finite Elements Section 3.1: Integral equations Section 3.2: Bounded linear operators 

15Feb 
Section 3.2: Bounded linear operators 

20Feb 
Section 3.3: Compact linear operators 

22Feb 
Section 3.3: Compact linear operators 

27Feb 
Section 3.4: Spectral theory for compact operators 

1Mar 
Section 3.5: Resolvent and pseudoresolvent kernels 

6Mar 
Section 3.5: Resolvent and pseudoresolvent kernels Section 3.6: Approximate solutions 

8Mar  Section 4.1: Delta functions  
13Mar  Section 4.1: Delta functions Section 4.2: Green's functions  
15Mar  Section 4.2: Green's functions  
3Apr  Section 4.3: Differential operators  
5Apr  Section 4.3.2: Adjoints of Differential operators  
10Apr 
Section 4.3.4: Fredholm Alternative for differential equations Section 4.4: Least squares solutions 

12Apr  Section 4.5: Eigenfunction expansions  
17Apr 
Section 4.5: Eigenfunction expansions Section 4.5.2: Orthogonal polynomials 

19Apr 
Section 6.1: Complex valued functions Section 6.2: The calculus of complex functions 
You are also encouraged to check out these suggestions from the Mathematics Department at
Harvey Mudd on
formatting homework assignments in
mathematics.
Due date  Problem set  Notes 
23Jan 
1.1: 1, 2, 7, 9a, 10 (also plot all 5 of the polynomials over [1 1]) 1.2: 1, 2a, 2b, 3, 4, 6a, 6d, 10a 1.3: 3 

1Feb 
1.4: 1, 4 1.5: 1bc, 2, 5, 14 2.1: 2, 3, 4 

24Feb  2.2: 1, 2b, 2c, 7, 8, 9, 14, 17, 20, 22, 25a  
15Mar 
3.1: 1 3.2: 2, 3 3.3: 1 3.4: 1, 2b, 3, 6 3.5: 1b, 2b 3.6: 4, 6 

5Apr 
4.1: 2, 5, 9, 11, 12 4.2: 1, 3, 6, 9, 13 

1May 
4.3: 1, 3, 6 4.4: 3, 7 4.5: 3, 6 6.1: 2 6.2: 4, 6, 12 