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 1:302:45pm, 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 handedin 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 4243: 2 (b) (c), 5, 7 (a) (b); (2.4) page 48: 7, 8; (2.5) page 56: 1; (2.6) page 61: 1.