MATH 674, PARTIAL DIFFERENTIAL EQUATIONS II
Spring 2005
Instructor:
Konstantina Trivisa:
 Office: 4103 Mathematics Bldg
 Phone: (301) 4055067
 Office Hours: (Fall 2004)
Tu, Th 9:00  10:15 or by appointment.
 Email:
trivisa@math.umd.edu
An introduction to the classical theory of PDE. The focus will be on
developing basic techniques to treat second order linear PDE such as
the Laplace equation, the heat equation and the wave equation, as well
as first order nonlinear PDE. The second semester will treat modern
methods for PDEs (distributions, functional analysis, Sobolev spaces,
bounded and compact operators in Hilbert spaces).
Prerequisites:
MATH 411 or equivalent.
Main Text:

Lawrence C. Evans,
Partial Differential Equations
The syllabus of Math 674/AMSC 674
consists of the core material in Chapters 5 and 6 and of selected topics from Chapters 4 and 79.
Further reading
Elliptic partial differential equations of second order by D. Gilbarg and
N. Trudinger
Partial Differential Equations by F. John
An Introduction to Partial Differential Equations by M. Renardy and C. Rogers
Partial Differential Equations by W. Strauss
Class Times: Tuesday and Thursday: 11:00am  12:15pm.
Location: MTH 1308
 COURSE OUTLINE
 Boundary value problems for elliptic partial differential
equations via operatortheoretic methods
 Hilbert spaces of functions
 Duality, weak convergence
 Sobolev spaces
 Spectral theory of compact operators
Grading (approximate):
 Homework: 40%
 Midterm : 30%
 Final: 30%
Assignments: Homeworks will be assigned and collected.