Classes are Tu-Th 4-5.30pm in AH 301. Office hours are Tu-Th
2.30-3.30pm in PGH696.
Prerequisites for this class are senior level real analysis or
equivalent, including metric space
topology and some results about Banach spaces, and a good course in
linear algebra.
This course will treat the material listed in the graduate course
description of the UH Mathematics
department. One of the Ph.D. preliminary exams is based on some of the
topics covered in this
Applicable Analysis sequence.
The fall semester will emphasize methods for proving the existence
of solutions of various classes
of equations. First the contraction mapping theorem will be decribed
and used to prove the
implicit and inverse function theorems, some existence theorems for
ordinary differential equations
andintegral equations. The second half of the semester will be
devoted to the solvability theory
of linear equations and an introduction to (real) Hilbert spaces. In
particular the Fredholm alternative will
be described and used in a variety of settings.
There is no required textbook for the course but the following books
have useful versions of some
of the material.
D. H. Griffel, Applied Functional Analysis, Dover 2002
A.W. Naylor and G.R. Sell, Linear Operator Theory in Engineering and
Science, Springer, 1982.
Grades in the course will be based on solutions of homework
problems.
Approximately every two
weeks,
some problems will be assigned.
If you have any questions, you may reach me at 713-743-3475 or send
e-mail
to
auchmuty@uh.edu.