Math 2900  PDEs I (Spring 2020)

Course Info:

 
Text:   Partial Differential Equations, by L. C. Evans, published by the American Mathematical Society. (Graduate Studies in Mathematics, 1st ed. 1998, 2nd ed. 2010. Either should be ok.)

Lecturer:   Ming Chen                               Email: mingchen@pitt.edu

                    Office: 601 Thackeray Hall         Office Hours: WF 10:00 AM - 11:30 AM,          Office Tel: (412) 624-8357

Class Meeting Times:    MWF 12:00 PM - 12:50 PM     524 Thackeray Hall

Grading:             Homework:          30%
                             Midterm:               30%
                             Final:                     40%

Useful references:

• Partial Differential Equations by Fritz John, Springer, 3rd ed. 1978.

• Elliptic Partial Differential Equations of Second Order by D. Gilbarg and N.S. Trudinger, Springer, 2nd ed. 1983.

Overview:

PDEs are ubiquitous in applications. They arise everywhere from the usual suspects, physics, chemistry, and biology, to less obviously related disciplines like economics and sociology. Phenomena like water waves, diffusion, shock waves, plasma physics, population dynamics - all of them are captured by PDEs. This course aims to survey some basic important topics in this subject. A list follows.

• Preliminaries. Examples of important PDEs. 

• The most important PDEs.

  1. Laplace's equation. Fundamental solution, mean value property, Green's function, energy estimates. Maximum principle, harmonic, subharmonic functions. Representation formulae, uniqueness, regularity.

  2. Heat equation. Fundamental solution, energy method, Duhamel's principle. Maximum principle, sub and supersolutions. Representation formulae, uniqueness, backwards uniqueness.

  3. Wave equation. Spherical means, method of descent, Duhamel's principle, energy methods. Representation formulae, uniqueness, domain of dependence.

• Distributions - basic properties. Convergence, derivatives, convolutions. Fundamental solutions of PDEs. Fourier transform.

• Sobolev Spaces.

Homework policies: 

Please try to complete the homework problems; the majority of your learning will come through completing the homework assignments and they can significantly impact your course grade. Students are encouraged to work together on homework. However, each student must turn in his/her own assignments and no copying from another student's work is permitted. Given the size of the course and the speed at which we're going to be moving, no late homework will not be accepted.

Announcement

Homework Problems

Due day

Problems

02/10/20 

                                               HW1                                               

03/02/20 　

                                               HW2                                               

04/20/20　　

                                               HW3