Daniel Phillips

MA 523: Introduction to Partial Differential Equations
Spring 2018, Purdue University


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.


Dan Phillips
Department of Mathematics
Purdue University

Contact Information:

Office: MATH 706
Telephone: (765) 49-41939
Email address: phillips@purdue.edu

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


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.)


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.

  • Please staple all loose sheets of your homework.

  • 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 (7-8:30 pm, Monday, March 19; REC 113). This will be based on Chapter 2 in [E], Practice Problems.There will be no lecture on the day of the exam.
    Final Exam: During Final Exam Week

    Grading Policy:

    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- Mar 5 ; Sec 3.2

  • Mar 5-23 ; Sec 4.6

  • Mar 26- ; [J] Partial Differential Equations, 3rd or 4th edition by Fritz John, Ch 2, Sec 5; Available online from the library.


  • 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.
  • Homework 4 solutions.
  • Homework 5 Due Mar 9.
  • Homework 5 solutions.