A tentative plan for the course:
1) Introduction
- Review: basic concepts from Analysis
2) Fourier Transform and Fourier Series (Chapters 1-4)
- Fourier Representation (Chapter 1)
- Convolution (Chapter 2)
- Fourier Transform Calculus (Chapters 3-4)
3) Fast Fourier Transform (Chapters 5-6)
4) Generalized Functions (Chapter 7)
5) Partial Differential Equations (Chapter 9)
6) Sampling (Chapter 8)
7) Wavelets (Chapter 10)
The chapters correspond to chapters in the textbook. The material will not always completely overlap the textbook.
This is a tentative plan and it is subject to changes both in terms of the topics and their order. In particular, you should expect adjustments in the topics of the second part of the course (that deals with applications).