Math 500 Fall 2004
Applied Analysis I
Professor J. Duan
E-mail: duan@iit.edu
Class Hours: Tu Th 10am--11:15am in E1 Room
Office Hours: Tu Th 2--3pm or by appointment
Applied analysis provides basic tools for interdisciplinary
applied mathematics. This course introduces fundamental concepts
and techniques of modern mathematical analysis. These
concepts and techniques are essential for modeling, analysis and simulation
of complicated phenomena in engineering and science.
This course is specially appropriate for graduate students who
would like to use applied analysis methods in their research,
or to learn such methods
for long term career development.
This course is application-oriented.
Examples from applications will be used throughout the course to
motivate and illustrate the concepts and techniques.
Not all materials will be presented, and students are
required to acquire some course materials by independent study.
Topics for Applied Analysis I include:
Metric spaces, vector spaces,
Banach spaces, Hilbert spaces, linear bounded (i.e.,continuous) operators, self-adjoint operators,
Banach fix-point theorems,
generalized Fourier series,
eigenvalue and spectral problems, principles of
linear functional analysis, compact operators, unbounded (i.e., discontinuous) operators,
Lebesgue measure, Borel measure,
probability measure, measurable functions, integration,
$L^p$ spaces, and
applications to mathematical modeling and analysis
in engineering and science.
Pre-requisite: Calculus and some basic
knowledge about linear algebra.
Textbooks:
1. Introductory Functional Analysis with Applications, by E. Kreyszig
2. Measure, Integral and Probability, by M. Capinski and E. Kopp