Math 144: Introduction to Fourier Analysis, Fall 2020

Instructor: Ioan Bejenaru

Office: AP&M 6230
E-mail: ibejenaru@ucsd.edu; Include Math 144 in the subject line.
Office Hours: Mo 3-4pm, Tu 3:30-4:30pm
I can also schedule appointments upon request. E-mail at the address above.

Teaching Assistant

Junekey Jeon

E-mail: j6jeon@ucsd.edu

Office hours: Tu 9-10am, Wed 9-10am

Announcements:

• All course information will be updated on this site and on Canvas.
• Final exam information. Material covered: Chapter 5; HW covered: 9,10 and 11
  
• Quiz 3 information. Material covered: Chapter 4; HW covered: 7,8, (parts of) 9; Important: This quiz will be open books+notes, but no other sources will be allowed.
  
• Quiz 2 information. Material covered: Chapter 2: sections 3,4,5 and Chapter 3 (not including 2.2 - A continuous function with divergent Fourier series); HW covered: 4,5,6
  
• Quiz 1 information. Material covered: Chapters 1: 1.2, 2.2 (steady state heat equation in the disc), Chapter 2: sections 1,2; HW covered: 1,2,3
  

  ---

  Prerequisites: Math 140B or Math 142B, or consent of instructor.

  Course description: Rigorous introduction to the theory of Fourier series and Fourier transforms. Topics include basic properties of Fourier series, mean square and pointwise convergence, Hilbert spaces, applications of Fourier series, the Fourier transform on the real line, inversion formula, Plancherel formula, Poisson summation formula, Heisenberg uncertainty principle, applications of the Fourier transform.

  Textbook: Fourier Analysis by E.M. Stein and R. Shakarchi. We will cover most of chapters 1-5.

  ---

  Homework: Homework will be assigned weekly. Homework is due every Thursday by 11pm and should be submitted on Gradescope. No late homework will be accepted. If, for any reason, you cannot turn in a homework assignment, keep in mind that the lowest score will be dropped.
  

  Quizzes: There will be three Zoom proctored quizzes on October 27th, November 17 and December 8 .

  Final exam: The final exam is scheduled for Thursday, December 17, 3-6pm. The actual format of the final is TBD.

  Exam policy (applies to HW, quizzes and final): given the online nature of this course, there will be several disclosed and undisclosed measure that I will take to ensure a fair grading policy. Cheating will be taken very seriously and automatically reported to the Academic Integrity Office.

  ---

  Grading: Your final score will be calculated as follows
  20% Homework + 20% Each Quiz (Total 60%) + 20% Final Exam

  Regrades: Graded Homework and Exams will be available on Gradescope. You have a week from the date the score has been posted for any one item (a homework, a quiz, the final) to submit a regrade request on Gradescope for that particular item. Any late regrade requests may not be considered.

  ---

  ---

  List of homework assignments:

  • Homework 1, due Oct 8: Chapter 1, exercises 1,2,5,7; Note: read and be familiar with exercises 3 and 4 (these are not to be handed in).
  • Homework 2, due Oct 15: Chapter 1, exercises 9,10,11 and Problem 1
  • Homework 3, due Oct 22: Chapter 2, exercises 1,2,3,6,9,10 and Problem 1 (a,b only); note: you can make use of Exercise 7 without proof.
  • Homework 4, due Oct 30: Chapter 2, exercises 12,15,16 and Problem 2
  • Homework 5, due Nov 5: Chapter 2, exercises 11,17,19; Chapter 3, exercises 2,5
  • Homework 6, due Nov 12: Chapter 3, exercises 8,9,11,12,13 and Problem 1
  • Homework 7, due Nov 22: Chapter 3, exercises 6,15,16 Chapter 4: exercises 1,5
  • Homework 8, due Nov 29: Chapter 4: exercise 7,8,9,10; Problem 2
  • Homework 9, due Dec 6: Chapter 4: exercise 11, Chapter 5: exercise 1,4,5,7
  • Homework 10, due Dec 10: Chapter 5: exercises 8,9,11,12 Problem 1; optional: Exercise 20 and Problem 2
  • Homework 11, not to be handed in: Chapter 5: 14,20,21;