MA52300: Introduction to Partial Differential Equations, Spring 2013

 

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)

HOMEWORK

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.

HW5: p.110: 2, 3, 4; p.125: 1, 4, 6 and this problem. Due 4/25, Thu. Solutions of some of them.

HW6 (will not be collected!): p. 145: 1, 2, 5, 7; p.153: 6, 7, 11.


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.    Solutions

Final Exam answers

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.


Other recommended books:

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, 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.