Math 2900:      Partial Differential Equations I Spring 2008

Instructor: David Swigon

Office: Thackeray 519, 412-624-4689, swigon@pitt.edu

Lectures:  MWF 10:00-10:50am, Thackeray 704

Office Hours: MW 1:00-3:00pm, Thackeray 519, or by appointment.

Course Web Page: http://www.math.pitt.edu/~swigon/math2900.html

Course Description

This is an introductory course to the classical theory of partial differential equations. The topics to be covered include the first order differential equation, the method of characteristics, linear second order equations including Laplace and wave equations, the heat equation, and various maximum principles, Cauchy-Kowalevski theorem, Dirichlet and Neumann boundary value problems.

Prerequisites

Advanced Calculus on the level of Math 1530,1540

Textbook

Primary

Fritz John, Partial Differential Equations, Springer, 1991. ISBN: 0387906096

Secondary

Gerald Folland, Introduction to Partial Differential Equations, Princeton University Press, 1995, ISBN: 0691043612

Grading Scheme

Homework assignments: 30%

Midterm exam: 30%

Final exam: 40%

Schedule

The precise schedule and a list of homework problems will be given out in advance and posted on the web. Homework is due in the beginning of a class one week after it was assigned.

Syllabus (tentative)

Date

Reading

Topics

Homework Assigned

Notes

Jan 7-11

 

Single First-order Equation

HW 1

 

Jan 14-18

 

Single First-order Equation

HW 2

 

Jan 21

 

NO CLASS

 

 

Jan 23-25

 

Second-order Equation

HW 3

 

Jan 28-Feb 1

 

Characteristic Manifolds and Cauchy Problem

HW 4

 

Feb 4-8

 

Cauchy-Kovalewski Theorem

HW 5

 

Feb 11-15

 

Laplace Equation

HW 6

 

Feb 18-22

 

Laplace Equation

 

 

Feb 25

 

Review

 

 

Feb 27

 

Midterm Exam

 

 

Feb 29

 

Hyperbolic Equations

 

 

Mar 3-7

 

Hyperbolic Equations in Higher Dimensions

HW 7

 

Mar 10-15

 

Spring Break No Classes

 

 

Mar 17-21

 

Hyperbolic Equations in Higher Dimensions

HW 8

 

Mar 24-28

 

Higher order Elliptic Equations

 

 

Mar 31-Apr 4

 

Parabolic Equations

HW 9

 

Apr 7-11

 

Parabolic Equations

HW 10

 

Apr 14-18

 

Parabolic Equations

 

 

Apr 23

 

FINAL EXAM