Math 295abc - Partial Differential
Equations
Class is scheduled for
MWF 3:00-3:50 in
MSTB 114
Office Hours MWF 2-3pm
Partial Differential Equations are a multifaceted subject with several
and deep connections to other areas of mathematics, such as differential
geometry, functional analysis, mathematical physics, applied mathematics,
harmonic analysis, ...
It should therefore not come as a surprise that a wide range of methods and
techniques have been developed for their treatment. This course is intended
to be an introduction and an overview highlighting the diverse aspects of
PDEs which make up its nevertheless organic body.
Fall quarter
-
Introduction and Motivation.
-
The theory of Distributions.
-
Fundamental Solutions.
-
Sobolev Spaces and Trace Theorems.
-
Weak Solvability Theory of Uniformly
Elliptic Boundary Value Problems.
-
Linear Evolution Equations I.
Assignments:
- Homework 5 (pdf)
- Homework 4 (pdf)
- Homework 3 (pdf)
- Homework 2 (pdf)
- Homework 1 (pdf)
Suggested Literature
All topics covered in class are also contained in
- L. C. Evans, Partial Differential
Equations , Graduate Studies in Mathematics Vol. 19, AMS 1998.
but other references can be more informative for specific topics:
- R. A. Adams, Sobolev Spaces,
Academic Perss 1975.
- R. Dautray, J. L. Lions, Mathematical
Analysis and Numerical Methods for Science and Technology, Vol. II,
Springer 1990.
- D. Gilbarg, N. S. Trudinger, Elliptic
Partial Differential Equations of Second Order, Springer, 1983.
- M. F. John, Partial Differential
Equations, Springer IV Ed 1982.
- J. L. Lions, E. Magenes, Non-Homogeneous
Boundary Value Problems and Applications I, II, III, Springer 1972/73.
- D. Mitrovic, D. Zubrinic, Fundamentals
of Applied Functional Analysis , Pitman Monographs and Surveys in Pure
and Applied Mathematics, Longman 1998.
- A. Pazy, Semigroups of Linear Operators
and Applications to Partial Differential Equations, Springer 1983.
- M. E. Taylor, Partial Differential
Equations, Volumes 1 and 3, Springer 1996.
- K. Yosida, Functional Analysis,
Springer 1980.