MATHEMATICAL SCIENCES DEPARTMENT

 

Spring Semester 2002-2003 (022)

 

MATH 538 : Applied Functional Analysis

 

Catalog Data            :            MATH 538: Applied Functional Analysis

 

Credit 3. A quick review of basic properties of Topoligical, Metric, Banach and Hilbert Spaces. Introduction to Hausdorff metric and iterated function systems. Fixed point theorems and their applications. Introduction to calculus in infinite dimensional spaces - Frechet and Gateau derivatives, Bochner Integral. Introduction to weak and w*-topologies. Algorithmic optimization including complementarity problems and variational inequalities.

Prerequisite: Math 411.

 

Textbook/

References::                1) A. H. Siddiqi      Applied Functional Analysis.

2) E. Zeidler  APPLIED FUNCTIONAL  ANALYSIS. Applications to Mathematical Physics

3) E. Zeidler  APPLIED FUNCTIONAL  ANALYSIS. Main Principles and Their Applications

 

 

Instructor                    Dr. M. El-Gebeily, Associate Professor, Mathematical Sciences.

 

Goals                          The course provides an essential overview of the main principles of functional analysis and their application to a wide variety of fields in physics, engineering, economics, … etc.

 

Prerequisites by topic:

 

1)         Basic properties of convergence of sequences in topological and metric spaces

2)         Basic theorems of analysis as covered in a course of advanced calculus

3)            Elements of linear algebra

4)         Basic definitions and manipulations in the calculus of several variables.

 

Topics

 

1)         Metric Spaces and Banach Fixed Point Theorem. (1 Class)

2)         Banach Spaces. (3 Classes)

3)         Hilber Spaces. (3 Classes)

4)            Fundamental Theorems. (4 Classes)

5)            Differential and Integral Calculus in Banach Spaces (3 Classes)

6)            Optimization Problems  (4 Classes)

7)            Operator Equations and Variational Methods (3 Classes)

8)            Variational formulation and approximation. (3 Classes)

9)            Variational Inequalities and Applications (4 Classes)

10)       Tests. (2 Classes)

 

Homework:

 

Homework problems will be assigned, collected and graded. Your homework grade will be based on the quality of the submitted work as well as the timely submission of the assignments.

 

Projects:

 

A term project will be assigned that includes the application of the above topics. Reports are required.

 

Grading:

 

The distribution of grade is as follows:

Classwork and projects                                                                                   40%

Major 1                                                                                                           15%

Major 2                                                                                                           15%

Final Exam (Compehensive)                                                                                 30%

 

Total                                                                                                                100%