Course Description:

(i) Fourier series and their properties;
(ii) inner products and orthogonality of functions;
(iii) separation of variations of boundary value problems;
(iv) Bessel functions;
(v) Orthogonal polynomials;
(vi) Fourier transforms;
(vii) Generalized functions;
(viii) Green's functions

Instructor:

Changyou Wang

Department of Mathematics

Purdue University

Contact Information:

Office: MATH 714

Email: wang2482@purdue.edu

Lecture Time and Place:

TR 3:00 - 4:15pm, REC 123

Office Hours:

TR 1:30-2:45pm, or by appointment

Textbook:

(All of the following are on reserve in math library.)

Main Text:
[E] Fourier Analysis and Its Applications, by Gerald B. Folland

Prerequisites:

Linear algebra, differential equations (ODEs), mathematical analysis (concepts of convergence)

Homework:

Homeworks will be assigned weekly and collected each Thursday starting from the second week of instruction.

Steps must be shown to explain your answers. No credit will be given for just writing down the answers, even if it is correct.

Please staple all loose sheets of your homework to prevent 5% penalty.

Please resolve any error in the grading (hws and tests) WINTHIN ONE WEEK after the return of each homework and exam.

No late homeworks are accepted (in principle).

You are encouraged to discuss the homework problems with your classmates but all your handed-in homeworks must be your own work.

Examinations: There will be one midterm exam and a final exam, both of which are in class.

Midterm Exam: During 8th week of class (February 28 ~ March 4): Thursday in class, March 3, 2022.

Final Exam: During Final Exam week/b>

Grading Policy:

Homeworks (50%)

Midterm Exam (20%)

Final Exam (30%)

You are expected to observe academic honesty to the highest standard. Any form of cheating will automatically lead to an F grade, plus any other disciplinary action, deemed appropriate.

Course Outline:

Course Progress and Announcement:

(You should consult this section regularly, for homework assignments, additional materials and announcements.)

Week 1: January 11, 13 (TR) : Examples of PDEs: heat, Laplace, and wave equation; separation of variables and solutions by expansion of eigenfunctions of second order ODEs.

Homework #1 ( Due Thursday, January 20 ): (1.1) page 7: 1, 2, 3, 4, 6; (1.2) page 11: 5; (1.3) page 17: 3, 4.

Homework #2 ( Due Saturday, January 29 ): pdf file of HW#2

Homework #3 ( Due Saturday, February 5 ): (2.3) page 42-43: 2 (b) (c), 5, 7 (a) (b); (2.4) page 48: 7, 8; (2.5) page 56: 1; (2.6) page 61: 1.