MATH 4660-001 and C SC 4666-001: Numerical Analysis II
Spring 1998. University of Colorado Denver

PREREQUISITE:
Prerequisites: MATH 3191 and MATH 3200; programming experience
or with instructor's approval

HOURS: MW 5:30-6:45 pm,

INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo) 644. Phone: 556-8102.
Office hours: Tue 3pm - 6pm (or by appointment)
WWW: http://math.ucdenver.edu/~aknyazev

Students are welcome to communicate with each other and the teacher on-line using the Web page
http://math.ucdenver.edu/~aknyazev/teaching/98/4660/comments

TEXTBOOK:
NUMERICAL ANALYSIS 6th Edition by Richard L. Burden and J. Douglas Faires Brooks/Cole Publishing Company, 1997

SUBJECT:
Methods for solving mathematical problems on the computer. Applications of approximation theory and optimization theory. Ordinary and partial differential equations.

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.

• Ch. 7. ITERATIVE TECHNIQUES IN MATRIX ALGEBRA. Norms of Vectors and Matrices. Eigenvalues and Eigenvectors. Iterative Techniques for Solving Linear Systems. Error Estimates and Iterative Refinement.
• Ch. 9. APPROXIMATING EIGENVALUES. Linear Algebra and Eigenvalues. The Power Method.
• Ch. 8. APPROXIMATION THEORY. Discrete Least Squares Approximation. Orthogonal Polynomials and Least Squares Approximation. Chebyshev Polynomials and Economization of Power Series.
• Ch. 10. NUMERICAL SOLUTIONS OF NONLINEAR SYSTEMS OF EQUATIONS. Fixed Points for Functions of Several Variables. Newton's Method. Quasi-Newton Methods. Steepest Descent Techniques.
• Ch. 5. INITIAL-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS. The Elementary Theory of Initial-Value Problems. Euler's Method. Higher-Order Taylor Methods. Runge-Kutta Methods.
• Ch. 11. BOUNDARY-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS. The Linear Shooting Method. Finite-Difference Methods for Linear Problems. The Rayleigh-Ritz Method.
• Ch. 12. NUMERICAL SOLUTIONS TO PARTIAL-DIFFERENTIAL EQUATIONS. Elliptic Partial-Differential Equations. Introduction to the Finite-Element Method.

• Ch. 7,9. 7.1: 2,4. 7.2: 1,2,4 7.3: 1(a,b),2(a,b) 7.4: 1(a,b) 9.1: 1,2(a),3(a,b) 9.2: 1(a,b),3(a,b)
  Due March 9, 1998
• Ch. 8. 8.1: 1,2,5(a,b,d,e,f),7(a) 8.2: 1(a-d),2(c,d), 7,8(a-d),9(c,d)
  Due March 23, 1998
• Ch. 10. 10.1: 5(a,b), 10.2: 1(a,b), 10.3: 1(a,b), 10.4: 1(a,d) - only two steps
  Due April 20 (extended to coming Monday!), 1998
• Ch. 5. 5.1: 2(a), 5.2: 3(a) - two steps, 5.3:2(b), 5.4: 10(b) - one step.
  Due May 4, 1998

• Midterm Project, Due March 25, 1998
• Final Project, Due May 11, 1998

TESTS: On Ch. 7-9. March 30, 1998 - On Ch. 5,10. May 6, 1998

Grading: 5% for every homework, 20% for every test and project.

Comments: Projects reports should be put on student's Web pages. Students are responsible for learning the Internet and MATLAB on their own. I will try to avoid discussing such issues in class.

Extra course materials: ODE, Linear Algebra, Optimization, Numerical Analysis I, Numerical Analysis II,
Numerical Methods for Engineers, Numerical Analysis, UNIX Survival, UNIXHelp, MATLAB, MathTools,
Newton's method, Numerical Recipes , Our Computer Lab
A Brief Course on Numerical Analysis (In Russian, KOI8-R)

Important Dates:
March 16-21 - Spring Break, April 6 - Last day to drop without Dean's approval