| Instructor: | Plamen Stefanov |
| Office: | MATH 448 |
| Email: | stefanov@math.purdue.edu |
| Phone: | 49-67330 |
| Meeting: | TueThu 12:00– 1:15, UNIV 217 |
| Office Hours: | click here |
| Grader: | Raphael Hora |
| Book | Robert McOwen, Partial Differential Equations: Methods and Applications (2nd Edition) |
HW1, due Tue, Jan.22, in class. Solutions
HW2, due Thu, Jan.31, in class. Think of it as a set of practice problems for Exam 1. Solutions (updated 2/7)
HW3, due Feb. 26 in class. Some answers
HW4: from the book: p.72: 13, 16; p.82: 1, 4, 6; p.90: 1, 2; p.94: 1, 2, 4ac. For 4ac, use the method on p.91, not the one on p.93. Due April 2, Tue. Solutions of some of them.Exam 1: Thu 01/31/2013, 8:00 - 9:30 pm, KNOY B033 Solutions
Exam 2: Tue 03/05/2013 8:00 - 9:30 pm, KRAN G020, open book, covers the material up to Chapter 2, fundamental solutions included Solutions
Exam 3: Tue 04/09/2013 8:00 - 9:30 pm, KNOY B033. Open book, will cover Chapter 3 and Chapter 4 up to 4.1(c), included.
Qualifying Exams Archive Characteristics (supplemental material)
Canceled classes: (to compensate for the exams): 2/28 (but we still have an exam that day!), 3/7 and 4/23.
PROBLEM SETS:
Weekly problem sets will be posted on this page.
MIDTERMS:
Three evening midterm exams will be given (so that you will have more than the
standard 50 min, I am aiming for 90 min).
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 (will be updated regularly)
Introduction
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
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, more...
4. The Laplace Equation
Fundamental Solution, Poisson's Formula,
Maximum/Mean Value Principle
more...
5. The Heat Equation
Heat Kernel, Maximum Principle, Energy Estimates
6. Functional Analysis Methods
Separation of Variables
Eigenfunctions Method
Fourier Transform