MTH 490003: Introduction to Fourier Analysis
Schedule and Topics Covered
Date  Topic/Section  Assignments and Reading  
1/12  Genesis of Fourier Analysis  Read Syllabus  
1/14  Fourier Series  Read Chapter 1 of Stein and Shakarchi  
1/19  Fourier Series  Read Section 2.1 of Folland Due 1/28: Homework 1 

1/21  The Dirichlet Kernel  Pick Project, Form Your Group  
1/26  Convergence of Fourier Series  Due 2/2: Submit References for Project (typed w/ LaTeX). Include (i) Project Topic, (ii) A paragraph detailing what you will study/do, (iii) Group members + PIDs, and (iv) A list of scholarly references (books, journal articles, etc.) you will start with. Four or five references will do for now.  
1/28  Convergence and Smoothness Homework 1 Due Today!  Read Sections 2.2 and 2.3 of Folland Due 2/9: Homework 2 

2/2  More on Convergence Project References Due Today!  Read Section 2.6 of Folland  
2/4  Fourier Series on Intervals, and Interpolation  Read Section 2.4 of Folland  
2/5  Last full day to drop with tuition refund.  
2/9  Hilbert Spaces Homework 2 Due Today!  Read Sections 3.1 and 3.2 of Folland Due 2/18: Homework 3 

2/11  Hilbert Spaces, L^{2}([a,b]), Conv. in Norm  Read Section 3.3 of Folland Due 2/18: Resubmit References for Project (typed w/ LaTeX). Address all instructor comments. Reform groups as necessary. Add a paragraph explaining your research plan. This will be graded as homework. 

2/16  Dominated Convergence Thm, Convolutions  Read Sections 3.4 and 7.1 of Folland  
2/18  Convolutions and Mollifiers Homework 3 Due Today!!! Revised Project Refs Due!!!!!!  Due 3/1: Homework 4  
2/23  Smooth f are dense in L^{2}  Read Section 7.2 of Folland  
2/25  Fourier Inversion  FOR FUN: Register to vote March 8  
3/1  Plancherel Theorem Homework 4 Due Today!  Due 3/15: Homework 5  
3/2  Last full day to drop with no grade reported.  
3/3  The Sampling Theorem  Read Section 7.3 of Folland Due 3/17: Submit a detailed outline of your project report. Add it to your previous references document (suitably revised). Make sure to say which group members will be responsible for each outlined section/project component. 

3/8  Spring Break  no class  FOR FUN: Vote in primary today  
3/10  Spring Break  no class  
3/15  Gabor Bases  
3/17  Distributions Homework 5 Due Today! Project Outline Due Today!  Read Section 9.1 of Folland Due 4/7: Turn in a rough draft of your report and slides for comments! Make it as complete as you can. Include a separate cover sheet listing the roles of each group member: Who took charge of writing/editing the first draft of each section? Who made sure all sections were integrated well together? Who is leading the work on the presentation slides? Who is coordinating to make sure all group members understand the the report as a whole? 

3/22  Distributions  Seriously: Work on your report while you have the chance!  
3/24  Distributions  Read Section 9.2 of Folland  
3/29  Weak Convergence  Work on reports and slides!  
3/31  Convolutions  Due 4/12: Homework 6  
4/5  Fourier Series  Read Section 9.3 of Folland  
4/7  Schwartz Functions Rough Draft of Report and Slides Are Due Today!!!  Read Section 9.4 of Folland  
4/12  Tempered Distributions Homework 6 Due Today!  Due 4/21: Homework 7  
4/14  Wrap Up, Presentation  Presentation (M.Dolinar) Attendance Required 

4/19  Project Presentations  JPEG and Chebyshev/Legendre Presentations Attendance Required 

4/21  Project Presentations Homework 7 Due Today!  Gravity Waves and Gen. Sampling Thm. Presentations Attendance Required 

4/26  Project Presentations  FFT and MRI Presentations Attendance Required 

4/28  Project Presentations  Algebra and Audio Compression Presentations Attendance Required 

5/2  Final Exam Time  12:45pm  2:45pm FINAL REPORTS, SLIDES, AND ANY CODE ARE ALL DUE BY 2:45pm TODAY! SLIDE PHYSICAL COPIES OF REPORTS UNDER MY OFFICE DOOR BEFORE 2:45pm. ALSO EMAIL CODE, SLIDES, AND ALL .TEX FILES TO ME BEFORE 2:45pm. And then, have a nice summer! 