MA 523: Introduction to Partial Differential Equations
Fall 2015, Purdue University
Course Description:

Introduction to basic concepts of partial differential equations through
concrete examples such as Laplace, heat, and wave equations, and first
order linear and nonlinear equations. The emphasis is on derivation of
"explicit" solution formulas and understanding the basic properties of
the solution. This course is different from a standard course of PDEs
for upper level undergraduate students, which uses mainly separation of variables and Fourier series.
This course prepares graduate students in the Department of Mathematics
for a written qualifying exam.
Instructor:
 Changyou Wang
 Department of
Mathematics
 Purdue University
Contact Information:
 Office: MATH 714
 Email: wang2482@purdue.edu
Lecture Time and Place:
 TR 12:00  1:15pm, REC 307
Office Hours:
 TR 2:003:30pm, or by appointment
Textbook:

(All of the following are on reserve in math library.)
Main Text:
[E] Partial Differential Equations, by Lawrence C. Evans,
second edition
Reference:
[J] Partial Differential Equations, by Fritz John.
Prerequisites:

Good "working" knowledge of vector calculus, linear algebra, and
mathematical analysis. A prior course of ordinary differential
equations is useful.
(In Purdue, these materials are taught in MA 265, 266, 351, 353,
303, 304, 366, 510, 511, 440+442 and 504.)
Homework:

Homeworks will be assigned roughly biweekly.
They will be gradually assigned as the course progresses.
Please refer to the course announcement below.
 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:
 Midterm Exam: October 28, Wednesday: 8:0010:00pm, SC 277
 Final Exam: Fri 12/18 8:00a  10:00a HAAS G066
Grading Policy:
 Class Participation (5%)
 Homeworks (40%)
 Midterm Exam (20%)
 Final Exam (35%)
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:
 The course will cover most of [E] Chapter 2
(transport, Laplace, heat and wave equations) and
selected sections of Chapter 3 (nonlinear first order equation)
and Chapter 4 ("miscellaneous" concepts and methods of solutions).
Course Progress and Announcement:
 (You should consult this section regularly,
for homework assignments, additional materials and announcements.)
Aug 25 (Tuesday):
[E, Ch. 1] Introduction to notations;
[E, Appendix C.2] Divergence (GaussGreen) Theorem,
higher dimensional integration by parts.
Aug 27 (Thursday):
Derivation of minimal surface equations.
[E, Sec 2.1] first order linear partial differential equation with constant coefficients.
Sept 1 (Tuesday):
[E, Sec 7.2.5]
classification of second order equations.
[E, 2.2.1] Radially symmetric and fundamental solutions of Laplace equation, Poisson's equation
Sept 3 (Thursday): [E, 2.2.2] Meanvalue formulas.
Sept 8 (Tuesday): [E, 2.2.3 a, b] Properties of harmonic functions
Homework 1, due in class or before 4pm Tuesday, Sep. 8.
(Slide your homework under the door in case I am not there.)
Solution to Homework 1
Sept 10 (Thursday): [E, 2.2.3 c] Local estimates on harmonic functions
Sept 15 (Tuesday): [E, 2.2.3 c] Local estimates on harmonic functions (Analyticity, Harnack's inequality)
Sept 17 (Thursday): [E, 2.2.4] Green's function
Sept 22 (Tuesday): [E, 2.2.4] Green's functions and Poisson's formula for the half plane
Sept 24 (Thursday): E, 2.2.4] Green's functions and Poisson's formula for balls
Homework 2, due in class or before 4pm Thursday, Sep. 24.
(Slide your homework under the door in case I am not there.)
Solution to Homework 2
Sept 29 (Tuesday): [E, 2.2.5] Energy method
Oct 1 (Thursday): [E, 2.3.1] Heat equation/fundamental solutions
Oct 6 (Tuesday): [E, 2.3.1 c] Nonhomogeneous equation/Duhamel's formula
Oct 8 (Thursday): Maximum principle and uniqueness
Oct 15 (Thursday): [E, 2.3.3] Mean value formula
Homework 3, due in class or before 4pm Thursday, October 15.
(Slide your homework under the door in case I am not there.)
Solution to Homework 3
Oct 20 (Tuesday): [E, 2.3.3] Properties of solutions
Oct 22 (Thursday): [E, 2.3.4] More on energy methods
Oct 27 (Tuesday):
Review for Midterm Exam (810pm, Wednesday, October 28, SC 277)
Homework 4, due in class or before 4pm Thursday, October 29.
(Slide your homework under the door in case I am not there.)