Math 19 Fall 2007 Schedule (also see the syllabus)

Prof. Tanya Leise

MWF 1pm Mudd203 and Tues 10am Mudd014

If you have the uncorrected 2002 printing of the Walnut text, use this list of errata to correct your text. (New copies will be the corrected version.)

Date
Topic
Homework/Handouts/Links
9/4-9/7

 
T
Introduction (in 014)

Treat Chapter 1 as reference; I will introduce needed concepts as we go along.

Hearing and graphing Fourier series

W
2.1 Trig series  
F
2.1 cont'd Intro Exercises (due Wed 9/12)
9/10-9/14

 
M
2.1 Convergence

2.25,2.26 (due Fri 9/14)

T
Lab 1 Convergence of FS (email by 10am Tues 9/18)
W
Series and norms Exercises on norms (due Fri 9/14)
F
2.2 Approx Identities 2.38, 2.41(a,c,e) (due Fri 9/21)
9/17-9/21

 
M
2.3 Generalized Fourier Series 2.60, 2.63 (due Fri 9/21)
T
Lab 2 Heat equation (email by 10am Tues 9/25)
W
2.3 cont'd
2.66, 2.67 (due Fri 9/28)
F
3.1 Fourier Transform
 
9/24-9/28

 
M
3.2 Basic properties Fourier transform practice (due Wed 9/26)
3.10 (due Fri 9/28)
T
Lab 3 Fourier transform (email by 10am Tues 10/2)
W
3.3 Fourier inversion
 
F
3.4 Convolution

3.24,3.25(a) (due Mon 10/1)

10/1-10/5

 
M
3.5 Plancherel's Formula
3.6 L2 functions
 
T
Lab 4 (Will be out of town, so no formal lab meeting)
Linear Filters (due Wed 10/10)
W
Review
 
F

Exam 1: Sections 2.1-3.4


Fall Break

 
10/10-12
   
W
3.7 Smoothness vs Decay
3.8 Dilation, Translation, Modulation

Dido's Problem (due Mon 10/15)
3.38 (due Fri 10/12)

F

3.9 Bandlimited functions and sampling formula

3.52 (due Wed 10/17)
10/15-10/19

 
M

Uncertainty principle

Uncertainty principle
T

Lab 5

Sampling (email by 10am Tues 10/21)

W

4.1 Signals


4.6 (due Fri 10/19)

F
4.2 Systems

4.25,4.29a,4.30 (due Wed 10/24)

4.42(a),4.43 (due Fri 10/26)

10/22-10/26

 
M
4.2 Systems, cont'd
 
T

Lab 6 Fast Fourier transform

FFT exercise (due Tues 10/30)
W
4.3 Periodic signals and the discrete Fourier transform
 
F

5.1 Dyadic step functions


10/29-11/2

 
M

5.2 Haar system

5.7,5.17,5.18,5.20(b) (due Fri 11/2)
T

Lab 7

Haar series (email by 10am Tues 11/6)
W
5.3 Haar bases on [0,1]
5.28 (for scales 0 through 4) (due Wed 11/7)
F
5.4 Haar series vs Fourier series
5.31,5.32 (due Fri 11/9)
11/5-11/9

 
M
Jump discontinuity estimate
 
T
Lab 8
Haar transform (email by 10am Tues 11/13)
W
6.1 Discrete Haar Transform
6.7, 6.10 (due Mon 11/12)
F

6.1 Matrix form of DHT

 
11/12-11/16

 
M

6.3 Image analysis with DHT

 
T

Lab 9

DHT image analysis (email by 10am Tues 11/27)
W
Review
 
F

Exam 2: Sections 3.5-6.1

 
Thanksgiving

 
11/26-11/30

 
M

7.1 Systems of translates
7.2 Multiresolution analysis


7.8, 7.11(a) (due Mon 12/3)
T
Lab 10
Multiresolution analysis (email by 10am Tues 12/4)
W
7.3 Examples of MRA
 
F
MRA continued  
12/3-12/7

 
M
7.4 ON Wavelet bases
 
T
Lab 11
Wavelets in MRA(email by 10am Tues 12/11)
W
7.4 continued
 
F
7.4 continued
 
12/10-12/12

 
M
Review
 
T/W
Project meetings  

Final written project report due 4pm Fri 12/14

Take-home exam due 4pm Tues 12/18
(covers Chapters 5-7)