Math 2900:      Partial Differential Equations I Spring 2008

Instructor: David Swigon

Office: Thackeray 519, 412-624-4689,

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

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

Course Web Page:

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.


Advanced Calculus on the level of Math 1530,1540



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


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

Grading Scheme

Homework assignments: 30%

Midterm exam: 30%

Final exam: 40%


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)




Homework Assigned


Jan 7-11


Single First-order Equation

HW 1


Jan 14-18


Single First-order Equation

HW 2


Jan 21





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





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