MATH 4650-001 & SC 4656-001: Numerical Analysis I
Fall 2002, University of Colorado at Denver

IMPORTANT ANNOUNCEMETS:
Thanks for taking this class! Happy New Year!

Current enrollment to MATH 4650-001
Current enrollment to C SC 4656 001

PREREQUISITE:
MATH 2411 AND 3191; PROGRAMMING EXPERIENCE (such as CSC1401 or Math3250).

WHY TAKING IT:
Math 4650 (CSC4656) is required for the "Computer Science and Engineering" major, and the "Computer Science" and "Actuarial Science" options in the Mathematics degree and the Applied Mathematics degree (as well as some other programs).

OTHER SIMILAR CLASSES AT CU-DENVER THIS SEMESTER:
MATH 4650-002 & SC 4656-002: Numerical Analysis I
Math 5660/CS 5616 - Numerical Analysis I

HOURS: MW 4-5:15 pm, Science Building 203.

INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo Bldg) 644. Phone: (303) 556-8102.
Office hours: Tuesday 4-5 pm, or by appointment.
WWW: http://www-math.cudenver.edu/~aknyazev

TEXTBOOK: Numerical Mathematics and Computing, 4th Edition by Ward Cheney and David Kincaid.
Published by Brooks/Cole Publishing Company
Fourth Edition, 1999
ISBN 0-534-35184-0. 560 pages

SUBJECT: Methods for solving mathematical problems on the computer. Solution of linear and nonlinear equations, interpolation, and integration.

CONTENTS:
The class will follow the outline below, touching on each major topic in a depth that will be determined by the pace of the class. The dates are tentative and are not guaranteed.

  1. Introduction (Independent reading, not covered in class)
    1.0 Preliminary Remarks
    1.1 Programming Suggestions
    1.2 Review of Taylor Series

  2. Number Representation and Errors (August 19 - Sept. 9)
    2.1 Representation of Numbers in Different Bases
    2.2 Floating-Point Representation
    2.3 Loss of Significance

  3. Locating Roots of Equations (Sept. 11 - Sept. 16)
    3.1 Bisection Method
    3.2 Newton's Method
    3.3 Secant Method

  4. Interpolation and Numerical Differentiation (Sept. 18 - Oct. 9)
    4.1 Polynomial Interpolation
    4.2 Errors in Polynomial Interpolation
    4.3 Estimating Derivatives and Richardson Extrapolation

  5. Numerical Integration (Oct. 14 - Oct. 28)
    5.1 Definite Integral
    5.2 Trapezoid Rule
    5.3 Romberg Algorithm
    5.4 An Adaptive Simpson's Scheme
    5.5 Gaussian Quadrature Formulas

  6. Systems of Linear Equations (Oct. 30 - Nov. 20)
    6.1 Naive Gaussian Elimination
    6.2 Gaussian Elimination with Scaled Partial Pivoting
    6.3 Tridiagonal and Banded Systems
    6.4 LU Factorization
GRADING:
Midterm Test (on Ch. 2-3) - 20%,
Final test (on Ch. 4-6) - 20%.
Two Computer Projects - 20% each,
Take-home Quizzes - 20%.
The following distribution of grades is used:
A+ 95-100%, A 90-95%, A- 85-90%
B+ 80-85%, B 75-80%, B- 70-75%
C+ 65-70%, C 60-65%, C- 55-60%
D+ 50-55%, D 45-50%, D- 40-45%

OUTCOMES:
By the end of the semester you should be able to read, understand and apply numerical methods associated with the topics covered in the semester and to correctly solve associated problems at the level of our textbook.

COMPUTING:
Individual projects will be accepted in one of the following languages: Matlab, C, C++, Fortran and Java. My recommendation is to use MATLAB, since it can link executable files, it has graphics already built in and it is an interpretive language originally developed to handle mathematical problems. The students are invited to use the MERC lab. Please register for Math 1999 lab to reserve a computer. Each student will have an account on math (the name of the computer), and other (except for beowulf) Linux-based networked computers of the CCM graduate lab soon after the census date.

LINKS: