Instructor : J. Osborn
Grader: David Bourne
Prerequisite: AMSC/CMSC 466, MATH 410
Text: Introduction to Numerical Analysis, 3rd Edition, Stoer & Bulirisch
Topics
| 1. Interpolation and approximation |
| Polynomial Interpolation |
| Uniform Approximation |
| Piecewise polynomial interpolation |
| Least squares approximation |
| 2. Quadrature |
| Newton-Coates formulas |
| Peano kernel theorem |
| Rombberg integration; Euler-Maclaurin formula |
| Gaussian integration |
| Adaptive quadrature |
| 3. Eigenvalue Problems |
| General theory |
| Similarity transformations; Householder transformations |
| Rayleigh quotient |
| Singular value decomposition |
| Power and inverse power methods |
| QR algorithm |
| Eigenvalue perturbation theory |
| 4. Iterative Methods for Linear Systems |
| Classical methods |
| The conjugate gradient method |
Although the course is mainly theoretical, we will do some illustrative computing. This will be done with MATLAB. For information on Campus computing resources and on MATLAB, see the links below and Chs. 1, 2, 4, and 8 in Differential Equations with MATLAB by Coombes, et al., which is on reserve in the Engineering and Physical Science Library (under Osborn).
Grading Policy: Grades will be based on homework (40%), midterm exam (20%), and final exam (40%).
Honor Pledge: Students are asked to write and sign the Campus Honor Pledge, ``I pledge on my honor that I have not given or received any unauthorized assistance on this assignment/examination'', on each exam.
Make-up Policy: Make-up examinations will be given only in the case of an absence caused by illness, religious observance, participation in a University activity at the request of University authorities, or compelling circumstances beyond the student's control. If you miss an exam, please present convincing reasons for your absence (doctor's note,...) as soon as possible. If possible, an absence should be arranged before the exam.
Students With Disabilities: If you have a documented disability and wish to discuss academic accommodations, please contact me as soon as possible.
Midterm Exam: Thursday, April 1.
Final Exam: Friday, May 14, 8:00-10:00.
Click here for OIT related computing information.
Click here for home page of The Mathworks, makers of MATLAB; go here for technical support.
Click here for additional links to MATLAB information.
Due Dates:
Problems 1-7 are due February 17.
Problems 8-15 are due March 16.
Problems 16-24 are due April 20.
Problems 25-39 are due May 4.
Problems 40-43 are due May 14.
References: These books are on reserve in the Engineering and Physical Science Library
| An Introduction to the Approximation of Functions, T.J. Rivlin |