Math 1080:      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