MATH 3241 3.0 (same as COSC 3121 3.0)

Numerical Methods I

Fall Term 1998-99

• Section A: Vari D, Tu and Th 10:00 to 11:20
• Section B: 303 Stong College, MWF 10:30 to 11:20

Instructor: Martin Muldoon

1998-99 York Calendar Description: An introductory course in computational linear algebra. Topics include simple error analysis, linear systems of equations, nonlinear equations, linear least squares and interpolation. (Same as SC/AS/COSC3121.03.)
Prerequisites: One of MATH1010.03, MATH1014.03, MATH1310.03; one of MATH1025.03, MATH2021.03, MATH2221.03; one of COSC1540.03, COSC2011.03, COSC2031.03.

Expanded description The course begins with a general discussion of computer arithmetic and computational errors. Examples of ill-conditioned problems and unstable algorithms will be given. The first class of numerical methods we introduce are those for nonlinear equations, i.e., the solution of a single equation in one variable. We then turn to a discussion of the most basic problem of numerical linear algebra: the solution of a linear system of n equations in n unknowns. The Gaussian elimination algorithm will be discussed as well as the concepts of error analysis, condition number and iterative refinement. Then we discuss polynomial and spline interpolation. We then turn to the least squares methods for solving overdetermined systems of linear equations, with a brief introduction to approximation theory. The emphasis in the course will be on the how, why and when of numerical approximation techniques. We will also discuss the development of numerical algorithms, and the use of mathematical software.

The textbook is Numerical Analysis by Richard L. Burden and J. Douglas Faires, 6th ed, Brooks/Cole Publishing Company, 1997 [Parts of Chapters 1,2,6,3,7,8]