# Spring 2018

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]