AS/SC/ MATH 3241 3.0 F

Numerical Methods I

      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/COSC 3121 3.0.)
      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. We then turn to the least squares methods for solving overdetermined systems of linear equations. Finally we discuss polynomial interpolations. The emphasis in the course is on the development of numerical algorithms, the use of mathematical software, and the interpretation of the results obtained on some assigned problems.
      A possible textbook is R.L. Burden and J.D. Faires, Numerical Analysis (6th ed.), PWS, 1997.