# Math 4362, Partial Differential Equations

# Spring 2018

## John Zweck

## Course Materials

Syllabus

## Lecture Notes

1. What are PDE's?

2. Linear and Nonlinear Waves [Part I]

3. Linear and Nonlinear Waves [Part II]

4. Nonlinear Transport

5A. The Wave Equation: Derivation and d'Alembert's Formula

5B. The Wave Equation: External Forcing

6. Introduction to Fourier Series

7. Fourier Series [Part I]

8. Fourier Series [Part II]

9. Convergence of Fourier Series [Part I]

10. Convergence of Fourier Series [Part II]

11. Separation of Variables: Heat Equation [Part I]

12. Separation of Variables: Heat Equation [Part II]

13. Separation of Variables: Wave Equation

14A. Separation of Variables: Laplace's Equation [Part I]

14B. Separation of Variables: Laplace's Equation [Part II]

15. Generalized Functions and the Dirac Distribution

16. Green's Functions for Poisson's Equation in 1D and 2D

## Homework Assignments

Homework 1, Due Wed Jan 17

Homework 2, Due Wed Jan 24

Homework 3, Due Wed Jan 31

Homework 4, Due Wed Feb 7

Homework 5, Due Wed Feb 21

Homework 6, Due Wed Mar 7

Homework 7, Due Wed Mar 21

Homework 8, Due Wed Apr 4

Homework 9, Due Wed Apr 11

Homework 10, Due Wed Apr 18

Homework 11, Due Wed Apr 25

Extra Problems [Not Due]

## Exam Info

Info re Exam Two

Info re Final Exam

## Past Exams

S18, Exam 1

S18, Exam 1 Solutions

S18, Exam 2

S18, Exam 2 Solutions

S18, Final Exam

S18, Final Exam Solutions

## Demos and Matlab Code

Movies by Olver to accompany his book

Matlab code for movie of fundamental solution of heat equation
[Credit: W. Stanford]

Movie of fundamental solution of heat equation [Credit: W. Stanford],
[You Tube]

Matlab code for movie of plucked-string solution to wave equation

Movie of plucked-string solution of wave equation,
[You Tube]

Partial Sums of Fourier Series of Sawtooth function and Gibb's phenomenon [pdf]

Movie illustrating nonuniform convergence of Sawtooth function,
[You Tube]

SawtoothFourierSeries.m [Matlab function used to generate Sawtooth plots]