MA 523 Fall 2024

 Instructor  Plamen Stefanov
 Office  MATH 728
 Email  stefanov@math.purdue.edu
 Meeting  MWF 10:30 - 11:20 in PHYS 333
 Office Hours  WF  1:30 - 2:30
 Grader  Naxian Ni
 Book  Robert McOwen, Partial Differential Equations: Methods and Applications (2nd Edition)

Lecture Notes   Click on the three books icon to collapse the big left margin. Zoom in or out for a comfortable view.


Homework


Other recommended books: 

Problem sets:

Weekly problem sets will be posted on this page.

Midterms

Three evening midterm exams will be given, as follows.

Final exam

A Final Exam will be given during the Final Exam Week.

Course grade

Your course grade will be determined using the following distribution: HW: 30%; Midterms 16% each (48% total); Final: 22%.


Schedule 

1. First Order Equations
Quasi-linear equations. Method of Characteristics and the Cauchy problem for 1st order PDEs.
Transport equations, shocks formations, conservation laws.
General non-linear equations: the eikonal equation only.

2. Higher (mainly second) Order Equations
The Cauchy Problem,  The Cauchy-Kowalevski Theorem, The Lewy example, 
Characteristics. See this for characteristics in any dimension. 
Linear 2nd order PDEs, normal form in two dimensions
Weak solutions
Distributions and fundamental solutions

3. The Wave Equation
The 1D wave equation
Methods of Spherical Means, Kirchhoff’s formula in 3D
Hadamard’s Method of Descent, solution formula in 2D
Duhamel's Principle, Energy

4. The Laplace Equation
Separation of Variables, Green's identities
Fundamental Solution, Poisson's Formula,
Maximum Principle, Mean Values
Fundamental solution, Green's function and Poisson Kernel
The Dirichlet problem in a half-plane and in a ball
Existence theorems  

5. The Heat Equation
Heat Kernel, Maximum Principle and uniqueness
Separation of variables, smoothing property
Infinite speed of propagation.