CSE 541 - Elementary Numerical Methods - Spring 2011

Senior Lecturer: Igor Malkiman, Ph.D., Tue.,Thu. DL0369 5:30 - 6:48 PM (4805)

malkiman.2@osu.edu; igorm@cse.ohio-state.edu;

Office Hours:  TR after class. Rm. DL246.

Course newsgroup cse.course.cse541 is on server news.cse.ohio-state.edu. Use your CSE account id and password to connect with SSL password authentication.

Grader: Scott Bennington  bennington.28@osu.edu; Day: Mon. 4:30 PM; Wed. 1:30 PM Room CL420

submit directory is c541aa

Description

Survey of basic numerical methods including: number systems and errors of finite representation; solution of a single nonlinear equation; zeros of polynomials; interpolation; numerical differentiation and integration; solution of linear systems, solution of ODEs and systems of ODEs.

Objectives

Students will gain insight into methods for computing approximate solutions to mathematical problems that occur frequently in computer simulations and real world problems. Particularly:

• Familiarity with finite number systems in computer arithmetic.
• Familarity with fixed vs. variable precision.
• Familiarity with elementary numerical methods, as implemented in current software, for finding zeros of real functions, and real and complex zeros of polynomials, computing derivatives, computing definite integrals, solving linear systems, interpolating data, solving ODEs.

Text

Ward Cheney and David Kincaid,Numerical Mathematics and Computing, Sixth Edition, Brooks/Cole Publishing, 2008 or Fifth Edition, Brooks/Cole Publishing, 2004. You can find Errata for the 6th edition (click Errata on a left menu) and for the 5th edition of the textbook from the authors.

Calculator

Scientific graphic calculator is recommended for use to solve homeworks and and is required for use to solve the exams problems.

Maple

Maple software from MapleSoft is recommended for use to study numerical methods while working on homeworks and labs' problems. Maple programs' samples are presented on topics' web pages. Maple is available on Unix from your account and on Windows at Baker Systems.

Topics

0. Introduction.
1. Taylor's series. Ch. 1
2. Background: computer arithmetic; rounding errors, machine precision, machine representation, Ch. 2
3. Root finding. Ch. 3
4. Polynomial Interpolation Ch. 4.
5. Differentiation. Ch. 4
6. Integration. Ch. 5
7. Systems of linear equations. Ch. 6
8. Ordinary Differential Equations. Ch. 8
9. Monte Carlo Integration Ch.11
10. Smoothing of Data and the Method of Least Squares. Ch.10

Midterm

Final

Prerequisites: algebra, trigonometry, calculus, and programming.

Grading Policy: