Math 2025: Integral
Transforms and Their Applications, Fall 2010

Syllabus. Here

Exam
Dates:

Exam 1. Thursday September 30

Exam 2. Tuesday November 2

Final Exam. Wednsday December 8 (
3:00-5:00pm)

No-class
Holidays(2010):

Labor day-
Monday, September 6

Fall Holiday begins - October 22- 24

Thanksgiving- TH/F November 24-28

Last
day of class December 4

Course outline:

1. Functions Wavelets and signals.

2. Chapter 1 of the textbook.

3. Application of Wavelets: Section 2.2 of the textbook.

4. Chapter 4 of the book (some notes we will use Vector spaces, Subspaces, Vector spaces of functions.)

5. Linear Maps, inner products and norms, basis, Gram-Schmidt orthogonalization, orthogonal projections.

6. Discrete and Fourier Transforms: a note on Complex numbers, and Discrete and Fast Fourier Transforms

Exam1 Solution

Suggested homework problems:

Exercise 1.1, 1.2 (page 7)

Exercise 1.5, 1.7, 1.9, 1.10

Exercise 1.17, 1.18, 1.20, 1.22, 1.23,

Exercise 1.26, 1.28, 1.30, 1.32, 1.34,

Exercise 1.39, 1.40, 1.41, 1.42

Exercise 2.7 - 2.11.

Exercise 2.15, 2.16, 2.19, 2.20, 2.22

Exercise 2.24 - 2.27