Math 7313, Spring 2015
John Zweck
Course Materials
Syllabus
My colleague Jon Bell at UMBC has a very nice set of notes
for a first course on PDEs
which you may find helpful.
Lecture Notes
1. Introduction
1B. Overview of Results from Analysis (I)
1C. Overview of Results from Analysis (II)
2. The Diffusion Equation
3^-. A Short Primer on Fourier Series
3. Classical Solutions of the 1D Diffusion Equation
4. Uniqueness of Solutions of the Diffusion Equation
5. The Fundamental Solution of the Diffusion Equation
6. An Introduction to Distributions; The IVP for the Diffusion Equation
7. Non-homogeneous IVP for Diffusion Equation; Duhamel's Method
8. Elliptic Equations
9. Mean Value Theorem and Maximum Principle for Harmonic Functions
10. Properties of Harmonic Functions
11. The Fundamental Solution of Laplace's Equation
12. Green's Functions for Elliptic Equations
13. The Linear Transport Equation
14. First-Order Quasi-Linear Equations and the Method of Characteristics
15. Burger's Equation, Shocks, and Traffic Dynamics
16. The Wave Equation (mostly in 1D)
17. d'Alembert's Formula
18. Kirchoff's Formula
Homework Assignments
Hwk 1 (Due THURSDAY 22 Jan)
Hwk 2 (Due Tues 3 Feb)
Hwk 3 (Due Tues 10 Feb)
Hwk 4 (Due Tues 17 Feb)
Hwk 5 (Due Tues 24 Feb)
Hwk 6 (Due Tues 10 Mar)
Hwk 7 (Due THURS 2 Apr)
Hwk 8 (Due THURS 16 Apr)
Hwk 9 (Not Due, but if you want feedback submit by 10am Thursday May 8.)
Material for Review of Multivariable Calculus
Multivariable Calculus will play a major role in Math 7313.
If you feel a bit rusty on it, I recommend the
lecture notes and
homework problems
from my Math 2415 course, which covers Chapters 12-16 of Stewart's Calculus text.
The most relevant material is that covered in Lectures 2,5,7,9,10,11,13,17,21,22,24,25,26,28,29.
I also have a large collection of
past exams.
Additional Lecture Notes on Vector Calculus.