# Math 441/620 - Numerical Analysis

## Schedule

This schedule is designed to give you an overview of the material to be covered and is tentative in nature.
The chapter numbers refer to the text, Kendall E. Atkinson, An Introduction to Numerical Analysis, second edition, Wiley, 1989.
 Lecture Date Main Topic Chapter 1 Tu 01/30 Overview 2 Th 02/01 Gaussian elimination: LU factorization 3 Tu 02/06 Taylor's theorem, sources of error 1 4 Th 02/08 Interpolation: theory and practice 3 5 Tu 02/13 Interpolation: Newton divided differences 3 6 Th 02/15 Interpolation: piecewise polynomial interpolation 3 7 Tu 02/20 Interpolation: problems with equidistant nodes 3 8 Th 02/22 Numerical differentiation: methods and errors 5 9 Tu 02/27 Numerical differentiation: effect of round-off 5 10 Th 03/01 Numerical integration: Newton-Cotes rules 5 11 Tu 03/06 Numerical integration: theory 5 12 Th 03/08 Numerical integration: Gaussian quadrature 5 13 Tu 03/13 Review 14 Th 03/15 Midterm exam Tu 03/20 Spring Break Th 03/22 Spring Break 15 Tu 03/27 Approximation: orthogonal polynomials 4 16 Th 03/29 Approximation: concepts and theory 4 17 Tu 04/03 Rootfinding: basic methods 2 18 Th 04/05 Rootfinding: theory of fixed-point methods 2 19 Tu 04/10 Systems of nonlinear equations: Newton's method 2 20 Th 04/12 Systems of nonlinear equations: Newton's method 2 21 Tu 04/17 Numerical o.d.e.'s: problem and basic methods 6 22 Th 04/19 Numerical o.d.e.'s: convergence of Euler's method 6 23 Tu 04/24 Numerical o.d.e.'s: stability of Euler's method 6 24 Th 04/26 Numerical o.d.e.'s: linear multi-step methods 6 25 Tu 05/01 Numerical o.d.e.'s: Runge-Kutta methods 6 26 Th 05/03 Numerical o.d.e.'s: methods for stiff problems 6 27 Tu 05/08 Computer numbers: basic prinples 1 28 Th 05/10 Computer numbers: IEEE-standard for floating-point numbers 1 29 Tu 05/15 Review