# Math 7313, Spring 2013

## John Zweck

## Course Materials

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.