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

Phone Number: 4-2719

Email: wang2482@purdue.edu

Lecture Time and Place:

TR 12:00 - 1:15pm, UNIV 117

Office Hours:

TR 1:45-3:00 pm, 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 weekly. 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 (homework problems and exams) 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:

Midterm Exam: Thursday, October 20, 12:00-1:15 pm, UNIV 117

Final Exam: TBA

Grading Policy:

Class Participation (5%)

Homeworks (40%)

Midterm Exam (20%)

Final Exam (25%)

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.)

August 23 (Tuesday):
[E, Ch. 2.1] Introduction to Linear Transport Equations

August 25 (Thursday):

[E, Ch. 2.1] first order linear partial differential equation with constant coefficients (continued)

[E, Ch. 2.2] Laplace's Equation

August 30 (Tuesday):

[E, 2.2.1] Radially symmetric and fundamental solutions of Laplace equation, Poisson's equation

September 31 (Thursday): [E, 2.2.2] Mean-value formulas.

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