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Math 222: Partial Differential Equations

TR 9:00-10:15 AM in COB 260: Syllabus (PDF)
Discussion Section: Fridays from 9:30 AM - 10:20 AM in COB 209
Office Hours: Tuesdays from 3:00 - 5:00 PM in COB 347 - NOTE THIS IS A CHANGE FROM THE SYLLABUS

Lecture 1 (01/19): Introduction to PDEs: including well-posedness, classification, and operators
(Chapter 1 Pinchover and Rubinstein and Chapters 1-2 Levy and Shearer)

Lecture 2 (01/21): Introduction to PDEs: including linear operators and superposition principle, mathematical models, and conditions
(Chapter 1 Pinchover and Rubinstein and Chapters 1-2 Levy and Shearer)
HW 1 Discussion Sections: 01/29 and 02/05
Additional problems will be added depending on how far in the material we get this week.

Lecture 3 (01/26): Introduction to PDEs: Boundary Conditions and First order equations: example and quasilinear equations

Lecture 4 (01/28): Method of Characteristics: Examples and General Theory

Lecture 5 (02/02): NO CLASS: Meet and work on extra homework problems

Lecture 6 (02/04): Method of Characteristics: General Theory, Theorem of existence and uniqueness, and Burger's Equation
HW 2 Discussion Sections: 02/12 and 02/19

Lecture 7 (02/09): Matlab examples, Derivation of Burger's Equation as a model of traffic flow
Linear transport matlab example
General initial curve matlab example
Exam 1 is moved to Thursday February 18 - CHANGE FROM SYLLABUS!

Lecture 8 (02/11): Burger's equation: time at which characteristics cross and weak solutions
(Section 2.7 Pinchover and Rubinstein and end of Chapter 3 and Chapter 13.1 Levy and Shearer)

Lecture 9 (02/16): Review and matlab examples
Levy and Shearer Problem 1.7 matlab example
Burger's Equation matlab example

Lecture 10 (02/18): Exam 1
HW 3 Discussion Sections: 02/26 and 03/04

Lecture 11 (02/23): Burger's Equation: Riemann Problem
(Section 2.7 Pinchover and Rubinstein and end of Chapter 3 and Chapter 13.1 Levy and Shearer)

Lecture 12 (02/25): Introduction to second order linear equations
(Chapter 3 Pinchover and Rubinstein and Section 2.2 Levy and Shearer)

Lecture 13 (03/01): Introduction to second order linear equations
(Chapter 3 Pinchover and Rubinstein and Section 2.2 Levy and Shearer)

Lecture 14 (03/03): Introduction to wave equation and general solution to wave equation
(Chapter 4 Pinchover and Rubinstein and Chapter 4 Levy and Shearer)
HW 4 Discussion Sections: 03/11 and 03/18

Lecture 15 (03/08): Wave equation: Cauchy problem, d'Alembert's formula, and characteristics
(Chapter 4 Pinchover and Rubinstein and Chapter 4 Levy and Shearer)

Lecture 16 (03/10): Wave equation: Domain of dependence and region of influence, inhomogenous Cauchy problem, and semi-infinite domain
(Chapter 4 Pinchover and Rubinstein and Chapter 4 Levy and Shearer)

Lecture 17 (03/15): Wave equation: energy and uniqueness of solutions
(Chapter 4 Pinchover and Rubinstein and Chapter 4 Levy and Shearer)
Wave equation matlab example

Lecture 18 (03/17): Introduction to heat equation and Fourier Series
(Section 2.4 Levy and Shearer and Section 1.4.1 Pinchover and Rubinstein)
(Separation of Variables and Fourier Series: Chapter 5 Pinchover and Rubinstein and Chapter 6 Levy and Shearer)
Exam 2 is moved to Tuesday April 5 - CHANGE FROM SYLLABUS!
Project 2 deadline is moved to Thursday March 31 - CHANGE FROM SYLLABUS!
HW 5 Discussion Sections: 04/1 and 04/8

Lecture 19 (03/29): Separation of Variables
(Chapter 5 Pinchover and Rubinstein and Chapter 6 Levy and Shearer)

Lecture 20 (03/31): Separation of Variables
(Chapter 5 Pinchover and Rubinstein and Chapter 6 Levy and Shearer)

Lecture 21 (04/05): Exam 2

Lecture 22 (04/07): Sturm-Liouville Theory: Inner Product Spaces and Orthonormal Systems
(Chapter 6 Pinchover and Rubinstein and Chapter 7 Levy and Shearer)
HW 6 Discussion Sections: 04/15 and 04/22

Lecture 23 (04/12): Sturm-Liouville Theory: Symmetric Operators, Convergence of sequences and series, Banach and Hilbert Spaces
(Chapter 6 Pinchover and Rubinstein and Chapter 7 Levy and Shearer)

Lecture 24 (04/14): Fourier Series Convergence
(Chapter 6 Pinchover and Rubinstein and Chapter 7 Levy and Shearer)

Lecture 25 (04/19): Fourier Series and Introduction to Laplace's and Poisson's equations
(Chapter 6 Pinchover and Rubinstein and Chapter 7 Levy and Shearer)
(Chapter 7 Pinchover and Rubinstein and Chapter 8 Levy and Shearer)

Lecture 26 (04/21): Laplace's and Poisson's equation: Fundamental solution
(Chapter 7 Pinchover and Rubinstein and Chapter 8 Levy and Shearer)
HW 7 Discussion Sections: 04/29 and 05/03

Lecture 27 (04/26):

Lecture 28 (04/28): Exam 3

Lecture 29 (05/03): Practice Presentations

Lecture 30 (05/05): Practice Presentations

Final Project Presentations
Tuesday, May 10, 2016 3:00 PM in COB 260

HOMEWORK SOLUTIONS
Homework 3: Problem 4
Levy and Shearer Chapter 4 Problem 5 and corresponding code
Pinchover and Rubinstein Problem 2.20
Pinchover and Rubinstein Problem 3.5
Levy and Shearer Chapter 13 Example 3