Math 2900: Partial Differential Equations I Spring 2008
Instructor: David Swigon
Office: Thackeray 519, 4126244689, swigon@pitt.edu
Lectures: MWF 10:0010:50am, Thackeray 704
Office Hours: MW 1:003:00pm, 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, CauchyKowalevski 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,
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 

Topics 
Homework Assigned 
Notes 
Jan 711 

Single Firstorder Equation 


Jan 1418 

Single Firstorder Equation 


Jan 21 

NO CLASS 


Jan 2325 

Secondorder Equation 


Jan 28Feb 1 

Characteristic Manifolds and Cauchy Problem 


Feb 48 

CauchyKovalewski Theorem 


Feb 1115 




Feb 1822 




Feb 25 

Review 


Feb 27 




Feb 29 

Hyperbolic Equations 


Mar 37 

Hyperbolic Equations in Higher Dimensions 


Mar 1015 

Spring Break – No Classes 


Mar 1721 

Hyperbolic Equations in Higher Dimensions 


Mar 2428 

Higher order Elliptic Equations 


Mar 31Apr 4 

Parabolic Equations 


Apr 711 

Parabolic Equations 


Apr 1418 

Parabolic Equations 


Apr 23 


