# Math 7313, Spring 2013

Syllabus

## Lecture Notes

1. Introduction
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 Tues 22 Jan)
Hwk 2 (Due Tues 29 Jan)
Hwk 3 (Due Tues 5 Feb)
Hwk 4 (Due Tues 12 Feb)
Hwk 5 (Due Tues 26 Feb)
Hwk 6 (Due Tues 5 Mar)
Hwk 7 (Due Tues 19 Mar)
Hwk 8 (Due Thurs 28 Mar)
Hwk 9 (Due Thurs 18 April)
Hwk 10 (Due Tues 30 April)
Hwk 11 (Optional, Not for Credit, Due Thurs 2 May)

## 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.