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