Lecture 
Date 
What was
covered 
Notes 
Textbook Section 
1 
Sep. 1 
Introduction 
 
1.1 
2 
Sep. 3 
Review of linear algebra: Linear independence, spanning sets, bases, norms 
get assignment 1 
1.1 
3 
Sep. 8 
Review of linear algebra: scalar product, orthonormal bases, l^p spaces 
 
 
4 
Sep.10 
Fourier series (I) 
return assignment 1; get assignment 2. Matlab Code 
1.3 
5 
Sep.15 
Fourier series (II): L^2 theory 
return assignment 2 
1.3 
6 
Sep.17 
Fourier series (III): pointwise convergence 
get assignment 3 
1.5 
7 
Sep.22 
Fourier series: Gibbs phenomenon. 
Matlab Code 
1.5 
8 
Sep.24 
Fourier transform: Examples 
return assignment 3; get assignment 4. 
3.1 
9 
Sep.29 
Rules for computing FT (I) 

3.2 
10 
Oct. 1 
Rules for computing FT (II); smoothnes vs. decay; Poisson summation formula 
return assignment 4; get assignment 5 
3.3(153),4.2(193),1.4 (3337) 
11 
Oct. 6 
sinecosine transforms; convolutions; integral equations 

Problem 1.3; 2.1,2.2, 2.3 
12 
Oct. 8 
convolutions  discrete signals & echo location 
return assignment 5; get assignment 6 
1.2 (1619), 2.3 (105106) , 2.4 
13 
Oct. 13 
Sampling of bandlimited signals; Sannon formula; reconstruction error (I) 

8.1, 8.2, 8.4 
14 
Oct.15 
Oversampling and reconstruction error (II) 
return assignment 6; get assignment 7 
8.2, 8.4 
 
Oct.15 
REVIEW SESSION 
MATH 0401 
2:00pm4:00pm 
15 
Oct.20 
Mid Term Exam 
MID TERM EXAM 
 
16 
Oct.22 
Generalized function: Schwartz class of test functions 

7.1 
17 
Oct.27 
Continuous and Slowly Growing (CSG) Functions. Derivative 
return assignment 7 
7.1 
18 
Oct.29 
Common Generalized Functions 
get assignment 8 
7.2 
19 
Nov. 3 
1/x , 1/x^{2} 

7.2 
20 
Nov. 5 
Translation, Dilation, Convolution, Products 

7.3 
21 
Nov. 10 
Derivative, Fourier transform 

7.3, 7.4 
22 
Nov.12 
Algebraic and Differential Equations 
return assignment 8, get assignment 9 
7.4 
23 
Nov.17 
Differential Equations(II) 

7.4 
24 
Nov.19 
Wave Equation 
return assignment 9, get assignment 10 
9.2 
25 
Nov.24 
Wave/Heat Equation 

9.2, 9.3 
 
Nov.26 
 
THANKSGIVING 
No Class 
26 
Dec. 1 
Heat Equation (II) 

9.3 
27 
Dec. 3 
ShortTime Fourier Transform (I) 
return assignment 10, get assignment 11 Matlab code
Pdf file 
11.2, 11.3, 11.4 
28 
Dec. 8 
ShortTime Fourier Transform (II) 

11.2, 11.3, 11.4 
29 
Dec.10 
Uncertainty Inequalities; Applied Harmonic Analysis 
return assignment 11; Last Class 
11.4, 12.4 (pg. 761) 
 
Dec.10 
REVIEW SESSION 
MATH 0305 
4:00pm6:00pm 
 
Dec.14 
FINAL EXAM 
FINAL EXAM 
8:00am10:00am 