MA 520: Boundary Value Problems Of Differential Equations
SPRING 2022, Purdue University

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>

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.