MATH 655: Elementary Numerical Analysis I
Syllabus - Fall 2002
Instructor: Marianne Korten
Office: Cardwell 234, 532-0567
Office Hours: MW 8:30 - 9:20 a.m.
Textbook: Kendall Atkinson, Elementary Numerical Analysis (Second edition)
Optional: Matlab, Student Edition
Syllabus:
1. Mathematical Preliminaries (two weeks):
The Taylor polynomial; The error in Taylor's polynomial; Computer
representation of numbers; Errors: sources, propagation.
2. Rootfinding (three weeks):
The bisection method; Newton's method; The secant method; Fixed point
iteration; Ill behaved rootfinding problems. 3. Interpolation and
approximation of functions (two weeks):
Polynomial interpolation; Divided differences; Errors in polynomial interpolation;
Interpolation using spline functions; The best approximation problem; Chebyshev
polynomials; A near-minimax approximation method. 4. Numerical integration
and differentiation (two weeks):
The Trapezoidal and Simpson rules; Error formulas; Gaussian numerical
integration; Numerical differentiation. 5. Solutions of systems
of linear equations. Systems of linear equations (three weeks):
Gaussian eliminations; Matrix arithmetic; The LU factorization; Error
in solving linear systems; Least squares data fitting. 6. Iterative
techniques in matrix algebras (two weeks):
The eigenvalue problem; Iteration methods; Nonlinear systems.
- Some computer experiments are performed in classes to show examples
of methods using Matlab. Students will also use programs in Matlab to do
some of the homework. They can use the lab to do the homework, or use a student
edition of Matlab at home with their own personal computers, or use Matlab
on the university UNIX system.
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Grading policy:
You must show all of your work in exams and homework in order to receive
full credit.
1. Homework counts as 30% of the final grade. Homework will be assigned
every class meeting, and will be due the next Wednesday at 4:30 in the
assigned mailbox. Late homework will only be accepted in exceptional
cases of illness or emergency.
2. A 50-minute midterm exam will count as 30% of the final grade.
3. A take-home final will count as 30% of the final grade.
4. Class partcipation (presenting solved problems to the class, attendance)
will count 10% of the final grade.
Math-Physics
Computer Classroom Laboratoty Hours
MIDTERM: 10/23
Sample midterm
Review for the final
- If you have any condition, such as a physical or learning disability,
which will make it difficult for you to carry out the work as I have outlined
it
- or which will require academic accommodations, please notify me in
the first two weeks of classes.
-
- ACADEMIC DISHONESTY: Plagiarism and cheating are serious offenses
and may be punished by failure on the exam, paper or project,
- failure in the course and/or expulsion from the University. For more
information refer to the academic dishonesty policy in `Inside KSU'.