Graduate Course Description
| Course Title: | Methods of Applied Mathematics, I |
| Unique Number: | M383C (59290) |
| Time/Location of Lecture: | MWF 10:00-11:00 am, RLM 12.166 |
| Instructor: | Professor Hans Koch |
Brief description:
An introductory course in linear Functional Analysis.
After some Preliminaries
(various spaces, properties, examples)
we will cover the basics on
Banach spaces
(continuous linear functionals and transformations;
Hahn-Banach extension theorem;
duality, weak convergence;
Baire theorem, uniform boundedness;
Open Mapping, Closed Graph, and Closed Range theorems;
compactness;
spectrum, Fredholm alternative),
Hilbert spaces
(orthogonality, bases, projections;
Bessel and Parseval relations;
Riesz representation theorem;
spectral theory for compact, self-adjoint and normal operators;
Sturm-Liouville theory),
and Distributions
(seminorms and locally convex spaces;
test functions, distributions;
calculus with distributions; etc.)
with examples and applications.
These are roughly the topics listed on the
Preliminary Exam Syllabus in Applied Math.
Textbook: None
Some References:
E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley & Sons, 1978.
J.B. Conway, A Course in Functional Analysis, Springer, 1990.
W. Rudin, Functional Analysis, McGraw-Hill, 1973.
M. Reed, B. Simon, Functional Analysis, Academic Press, 1980.
R. Meise, D. Vogt, Introduction to Functional Analysis, Oxford University Press, 1997.
K. Yosida, Functional Analysis, Springer, 1980.
H.L. Royden, Real Analysis, MacMillan, 1988.
S. Lang, Real Analysis, Addison Wesley, 1983.
J. Hunter, B. Nachtergaele, Applied Analysis, World Scientific, 2001.
Online, 2005.
T. Arbogast, J. Bona, Methods of Applied Mathematics,
Course Notes, 2005.
S. Serfati, Functional Analysis Notes,
Course Notes, 2004.
D.N. Arnold, Functional Analysis,
Course Notes, 1997.
P. Garrett, Functional Analysis,
Course Notes, 1996-2008.
W.W.L. Chen, Linear Functional Analysis,
Course Notes, 1983-2001.
R. E. Showalter, Hilbert Space Methods for Partial Differential Equations,
Online Book, 1994.
V. Liskevich, Measure Theory,
Course Notes, 1998.
L. Erdos, Notes on
Integration
and
Fourier transform.
Prerequisites: Familiarity with the subject matter of the undergraduate analysis course M365C and an undergraduate course in linear algebra.
Consent of Instructor: Not required
First Day Handout: Here
Homework: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
| Prof. H. Koch |
| RLM 12.152 |
| 471-8183 |
| Email: koch@math.utexas.edu |
| Homepage: http://www.math.utexas.edu/users/koch/ |