Math 501 Spring 2005
Applied Analysis II
Professor J. Duan
E-mail: duan@iit.edu
Class Hours: Tuesdays and Thursdays 10:00-11:15am in E1 Room
Office Hours: Tuesdays and Thursdays 1:30---2:30pm 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 material will be presented in class.
We will expect you to acquire some of the material. Our responsibility is to point out where you
should concentrate your study and to help pace your progress through the course.
Topics for Applied Analysis II include:
Partial Differential Equations ---
Examples of partial differential equations as mathematical models;
first order equations;
second order equations; wave equations; Laplace
equations; heat equation; numerical simulations via Matlab;
linear and nonlinear diffusion equations; strong and weak
solutions; well-posedness; Sobolev spaces; fixed point method;
method of semigroups of linear operators;
partial differential equations models in
engineering and science.
Pre-requisite: Calculus, elementary differential equations,
Math 500, or consent of the Instructor.
Textbook:
Partial Differential Equations: Methods and Applications. Robert
C. McOwen, Second Edition, Published by Prentice Hall, 2003.