Spring 2016: MATH 275

Basic Theory of Partial Differential Equations

Class: TR, 10:30am-11:50am in Eckhart 206 203
Instructor Office Hours: M 2:30-3:30pm, T 4-5pm

College Fellow: Seung uk Jang
College Fellow Office Hours: TW 7-8pm in Eckhart 28B
Problem Session: Wed 6-7pm, Eckhart 308

Course Syllabus

Text: Partial Differential Equations: An Introduction to Theory and Applications, Michael Shearer and Rachel Levy.

Notes on ODE Theory
Lecture 1
Lectures 2-3
Lecture 4: Harmonic Regularity and Liouville's Theorem and Green's Functions and Distributions
Poisson Kernel of the unit ball and Energy Methods also a supplement on the Poisson Formula for the half space.
Lecture 6
Lecture 7: Heat equation in bounded domains, maximum principle.
Lecture 8: Heat equation uniqueness in unbounded domain.
Lecture 9: Wave equation, D'Alembert's formula, finite speed of propagation, Dirichlet boundary conditions.
Lecture 10: Wave equation in 2 and 3 dimensions, Huygen's Principle.
Lecture 11 and Lecture 12: Method of characteristics.
Lecture 13: Scalar conservation laws.
Lecture 14: Travelling wave solutions of PDE.
Lecture 15: Intro to Hamilton-Jacobi Equations.
Lecture 15-17: Intro to Hamilton-Jacobi Equations (all lectures).

Homework: Homeworks will be posted here on Thursdays and due the next Thursday in class.

Homework 1
Homework 2
Homework 3
Homework 4
Homework 5
Homework 6
Homework 7
Homework 8

Exams: There will be one in-class midterm and a final exam. The midterm exam will be on Tuesday, April 26. The final exam will be on Tuesday, June 7, 10:30AM-12:30PM.

Grading: homework 30%, hour exams 40%, final exam 30%.