Lecture 
Date 
What was
covered 
Notes 
Textbook Section 
1 
Aug. 30 
Inroduction/Review of Analysis/Review of Linear Spaces with Scalar Product 
get assignment 1 
1.1 
2 
Sept.
4 
Review (cont.); Fourier Series  heat equation 
 
9.3 (548553) 
3 
Sept.
6 
Fourier series (I) 
turn in assignment 1 
1.3 
4 
Sept.
11 
Fourier series (II) 
turn in assignment 2

1.3 
5 
Sept.
13 
Fourier series (III): L^2 theory; Plancherel theorem;
mean square approximation error 
 
1.3, 1.5 
6 
Sept.
18 
Fourier series (IV): pointwise convergence, Dirichlet criterion; Gibbs Phenomenon; Numerical Approximations 
Matlab code: convergence, Gibbs; turn in assignment 3 
1.5 
7 
Sept.
20 
Fourier transform: Definition, L2 theory 
 
1.5 
8 
Sept.
25 
Rules for computing FT;sinecosine transforms; convolutions; integral equations 
turn in assignment 4 
3.1, 3.2; Problem 1.3 
9 
Sept.
27 
Differential equations; Poisson Sum formula 
 
3.2 
10 
Oct.
2 
Convolutions (1) 
turn in assignment 5 
2.1,2.2, 2.3 
11 
Oct.
4 
Convolutions (2) 
turn in assignment 6 
1.2,2.3,2.4,3.3(153),4.2(193) 
 
Oct. 5 
REVIEW SESSION 
3:005:00pm 
CSIC 4122 
12 
Oct.
9 
TEST 1 
 
 
13 
Oct.
11 
Sampling of bandlimited signals; Sannon formula; reconstruction error (I) 
 
8.1, 8.2, 8.4 
14 
Oct.
16 
Oversampling and reconstruction error (II) 
 
8.2, 8.4 
15 
Oct.
18 
Reconstruction error (III); Generalized Function: Schwartz class of test functions 
 
8.4, 7.1 
16 
Oct.
23 
Continuous and Slowly Growing (CSG) functions. 
turn in assignment 7 
7.1 
17 
Oct.
25 
Derivative of a distribution. Common generalized functions 
Class in CSI 1122 
7.2 
18 
Oct.
30 
Distributions: Derivative. Fourier transform 
CANCELED DUE TO HURRICANE SANDY 
see file 
19 
Nov.
1 
Distributions: 1/x and Fourier transform 
turn in assignment 8 
7.3 
20 
Nov.
6 
Distributions: Convolutions, Algebraic and Ordinary Differential Equations 
Class in CSI 1122 
7.3, 7.4 
21 
Nov. 8 
Applications of Fourier transform to distributions; Periodic distributions 
Class in CSI 1122; turn in assignment 9 
7.5, 7.7 
 
Nov. 9, noon 
TURN IN ASSIGNMENT 9 
CSI 4131 
 
 
Nov. 12 
REVIEW SESSION 
5:00pm7:00pm 
CSIC 4122 
22 
Nov.
13 
TEST 2 
 
 
23 
Nov.
15 
PDE: Wave Equation 
 
9.2 
24 
Nov.
20 
PDE: Heat Equation (I) 
 
9.3 
25 
Nov.
22 
No Class 
 
Thanksgiving Break 
26 
Nov.
27 
PDE: Heat Equation (II) 
 
9.3 
27 
Nov.
29 
Windowed Fourier Transform (I) 
turn in assignment 10 
11.2 , 11.3 , 11.4 
28 
Dec.
4 
Windowed Fourier Transform (II)/Wavelet Transform (I) 
Here is some Matlab code. 
11.4 
29 
Dec.
6 
Wavelet Transform (II) 
 
 
30 
Dec.
11 
Uncertainty Inequality; Instantaneous Frequency 
turn in assignment 11; Last Class 
 