# Daniel Phillips

MA 523: Introduction to Partial Differential Equations
Spring 2017, Purdue University

http://www.math.purdue.edu/~phillips/site/Courses/MA_52300-S17

Course Description:

First order quasi-linear equations and their applications to physical and social sciences; the Cauchy-Kovalevsky theorem; characteristics, classification and canonical forms of linear equations; equations of mathematical physics; study of Laplace, wave and heat equations; methods of solution.

Instructor:

Dan Phillips
Department of Mathematics
Purdue University

Contact Information:

Office: MATH 706
Telephone: (765) 49-41939

Lecture Time and Place:

M-W-F 9:30 - 10:20am ; REC 309

Office Hours:

M 10:30-11:20am, W 2:30-3:20pm or by appointment

Textbook: [E] Partial Differential Equations, by Lawrence C. Evans, second edition

Prerequisites:

Vector and advanced 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 or 504.)

Homework:

Homeworks will be assigned roughly bi-weekly. They will be assigned throughout the semester and posted here.

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

• 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:

Test: One evening exam (Monday, March 19). This will be based on Chapter 2 in [E].
Final Exam: During Final Exam Week

Homeworks (40%)
Test (25%)
Final Exam (35%)

You are expected to observe academic honesty to the highest standard.

Course Outline:

The course will cover most of [E] Chapters 1 and 2 (transport, Laplace, heat and wave equations), Section 3.2 (nonlinear first order equations), Section 3.4 (introduction to scalar conservation laws). parts of Chapter 4 (separation of variables, Fourier transform and power series methods) .

Course Log:

(You should consult this section regularly, for additional materials and announcements.)
• Jan 8; Sec 2.1

• Jan 10-31; Sec 2.2

• Feb 2-9; Sec 2.3

• Feb 9-21; Sec 2.4

• Feb 21-; Sec 3.2

Assignments:

• Homework 1 Due Jan 22.
• Homework 1 solutions.
• Homework 2 Due Feb 5.
• Homework 2 solutions.
• Homework 3 Due Feb 19.
• Homework 3 solutions.
• Homework 4 Due Feb 28.