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]