MATH 611 SYLLABUS

KING FAHD UNIVERSITY OF PETROLEUM & MINERALS

Department of Mathematical Sciences

Semester I, 2001-2002

** Course #**: Math. 611 - Hilbert Space
Methods in Applied Mathematics.

** Instructor**: Dr A. Boucherif.

** Textbook**:
I. Stakgold, Green s Functions and Boundary Value Problems, John Wiley & Sons,
New York, 1979.

** References**:

1. L. D. Kovach, Boundary Value Problems, Addison Wesley, 1984.

2. J. P. Keener, Principles of Applied Mathematics: Transformation and Approximation, Addison Wesley.

3. B. Friedman, Principles and Techniques of Applied Mathematics,

**
Objectives**: This course is designed to expose the students to
methods applicable to problems arising in the applied sciences. The method of
Green s functions is introduced through intuitive ideas and simple examples, and
then applied to the systematic study of two-point boundary value problems for
second and higher order differential equations. Metric and Hilbert spaces shall
be discussed in order to introduce the basic ideas of operator theory with
application to Volterra and Fredholm integral equations. Finally, the theory of
distributions will be presented in an elementary way.

Week |
Section # |
Topic |

1-2 |
Chapter 1 |
Green s functions: examples-properties |

3-4 |
Chapter 3 |
One dimensional boundary value problems |

5-8 |
Chapter 4 |
Metric and Hilbert spaces |

9-10 |
Chapter 5 |
Operator theory |

11 |
Chapter 6 |
Integral equations |

12-14 |
Chapter 2 |
Theory of distributions and related topics |

15 |
Reference Texts |
Applications |

** Grading Policy**:

-One mid-term exam.: 35 %

-One final exam (part I: take-home, part II: in-class): 45 %

-Assignments : 20 %