Download Approximation Theory

Approximation Theory
MATH 624 SA
Semester(I) 1434/35H 2013/14G
Instructor's Information
Instructor
Hanan Ali Batarfi, Dr.
Office
9c, Floor-2, Maths. Dept., Science Buliding (7)
Campus
Women's Campus-Main
Tel
+966-12-6952000 ext 26216
Email
[email protected]
Office Hours
Monday&Wednesday 1-3pm, Tuesday 11am-1pm+2 to 3pm
Course URL
TBA
Course's Basics
Credit
Theoretical
No. of Weeks
Student's catogary
3 hours
3 hours
Lab
1:30 hours
16
Seniors
Course Pre-requisite
MATH 621 or 622 Numerical Treatment of Simultaneous Linear Equations /or/
Numerical Treatment of OD Equations
Course Objectives
1
Systematic study of the different approximation methods and/or theories,
2
A study of few application of these methods and/or theories in real life
3
Computational study and numerical evaluation of the approximations and the
involved error
Course Grading
Seminar 1
Seminar 2
Seminar 3
Seminar 4
Project 1
15%
15%
15%
15%
40%
Seminar's/Project Topic
Seminar 1
Some Methods in Approximation Theory: A seminar given to
the PG students and researcher in Faculty of Science, the
seminar covers some real life model/experimental applications.
A Maple programming and numerical results are discussed
Seminar 2
De La Valee-Poussin Approximation and its Application
Seminar 3
TBA
Seminar 4
TBA
1
Project 1
Multivariate Pade' Approximation for Solving
Course Flow
Week Topic
1
2
Best approximation in Normed space, ch.1 in [1]
3
Least Square (LS) Approximation, sec.8.1 in [3] and
[3]
4
Orthogonal Polynomials, ch.8 in [1] and [4]
5
Orthogonal Polynomial and LS Approximation, Sec.
8.2 in [2] and [3]
6
Eid AlAdh'ha
7+8
Chebyshev Polynomial:
(a)Characterization in [3] pp31-43 and
(b)Economization of Power Series in [2], sec.8.3.
9
De La Valee'-Poussin in [4], lec.4
10+11 Rational Function in sec.8.4 [2]:
-Pade' Approx in [2]+[4]
-Continued Fraction and Chebyshev Poly.
12
Spline Function and Approximation in [4], lec.10/11
13+14 Multivariate Approximation
15
16
17
Final
Seminar's date/time
Seminar 1
Tues 24/12/1434H
Project 1
References/Supplementary Reading
[1] "A Short Course on Approximation Theory", N. L. Carothers, Bowling Green
State University, Lecture notes.
[2] "Numerical Analysis", Richard Burden and J. Douglas Faires, 8th Ed. (Thomson
Brooks-Cole, 2005)
[3] "Approximation Theory", Massoud Malek
(http://www.mcs.csueastbay.edu/~maleklclasslapprox.pdf); "Numerical
Approximation", Carmen Are'valo and clan Fuhrer,
http://www.maths.lth.se/na/courses/numa12/
[4] "Son of Afternotes on Numerical Analysis", G. W. Stewart, Lectures' Series,
University of Maryland, 1996.
2