Department of Mathematics

MTH 490-003: Introduction to Fourier Analysis

Schedule and Topics Covered

Date Topic/Section Assignments and Reading
1/12Genesis of Fourier Analysis-Read Syllabus
1/14Fourier Series-Read Chapter 1 of Stein and Shakarchi
1/19Fourier Series-Read Section 2.1 of Folland
-Due 1/28: Homework 1
1/21The Dirichlet Kernel-Pick Project, Form Your Group
1/26Convergence 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.
1/28Convergence and Smoothness
-Homework 1 Due Today!
-Read Sections 2.2 and 2.3 of Folland
-Due 2/9: Homework 2
2/2More on Convergence
-Project References Due Today!
-Read Section 2.6 of Folland
2/4Fourier Series on Intervals, and Interpolation-Read Section 2.4 of Folland
2/5Last full day to drop with tuition refund.
2/9Hilbert Spaces
-Homework 2 Due Today!
-Read Sections 3.1 and 3.2 of Folland
-Due 2/18: Homework 3
2/11Hilbert Spaces, L2([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.
2/16Dominated Convergence Thm, Convolutions-Read Sections 3.4 and 7.1 of Folland
2/18Convolutions and Mollifiers
-Homework 3 Due Today!!!
-Revised Project Refs Due!!!!!!
-Due 3/1: Homework 4
2/23Smooth f are dense in L2-Read Section 7.2 of Folland
2/25Fourier Inversion-FOR FUN: Register to vote March 8
3/1Plancherel Theorem
-Homework 4 Due Today!
-Due 3/15: Homework 5
3/2Last full day to drop with no grade reported.
3/3The 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 E-MAIL CODE, SLIDES, AND ALL .TEX FILES TO ME BEFORE 2:45pm. And then, have a nice summer!