King Fahd
University of Petroleum and Minerals
Department of Mathematical Sciences
MATH 514 Advanced Mathematical Methods
Semester II, 2003-2004 (042)
Dr. F. D. Zaman
Text Book: James P. Keener, Principles of Applied Mathematics
(Addison Wesley Publishing Company)
Additional
Objectives: This course is designed to introduce advanced
mathematical methods to graduate students in Mathematics, Science and
Engineering.
Bulletin Description: Integral transforms;
Fourier, Laplace, Hankel and Mellin transforms and their applications. Singular
integral equations. Wiener Hopf technique. Applications of conformal mapping.
Introduction to asymptotic expansions.
|
Week |
Date |
Chapter |
Topic |
|
1 - 2 |
Feb. 12 23 |
6.1, 6.2 |
Review of Complex integration. Branch points and
integration along branch cuts. |
|
3-4 |
Feb.26Mar 9 |
7.2 |
Fourier and Laplace transforms, analyticity of transforms
and inversion. |
|
5-6 |
Mar. 12 23 |
Additional material |
Applications of Fourier and
Laplace transforms. |
|
7 |
Mar. 26 30 |
7.3 |
Hankel transform; properties
and applications |
|
8 |
Apr. 2 6 |
Additional material |
Mellin transform; properties
and applications |
|
April 7 15 : Midterm Break |
|||
|
9 |
Apr. 16-20 |
3.1, class notes |
Singular integral equations |
|
10 |
Apr.23 27 |
Additional material |
Wiener-Hopf method for singular
integral equations |
|
11 |
Apr.30-May4 |
Additional material- |
Wiener-Hopf method for mixed
boundary value problems |
|
12 |
May 7 11 |
6.3 |
Conformal mappings;
applications. |
|
13 |
May 14 18 |
10.1 |
Little o and big O symbols;
asymptotic functions |
|
14-15 |
May21June1 |
10.2, 10.3 |
Asymptotic sequences and
series. Asymptotic approximation of integrals. |
Office: 5 - 430 Phone 2189
Email: fzaman@kfupm.edu.sa
|
Major # 1 |
25 % |
|
Major # 2 |
25 % |
|
Assignments/Attendance |
15 % |
|
Final |
35 % |