# Math 441/620 - Numerical Analysis

## Detailed 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.
 Class Date Main Topic Section(s) 1 We 08/31 Overview Mo 09/05 Labor Day 2, #1 We 09/07 Gaussian elimination: LU factorization 8.1 3 Mo 09/12 Taylor's theorem in one dimension 1.1 4 We 09/14 Taylor's theorem in higher dimensions 1.1 5, #2 Mo 09/19 Interpolation: existence and uniqueness 3.1 6 We 09/21 Interpolation: Newton divided differences, error theorem 3.2 7 Mo 09/26 Interpolation: problems with equidistant nodes 3.5 8, #3 We 09/28 Interpolation: cubic spline interpolation 3.7 9 Mo 10/03 Numerical differentiation: idea and methods 5.7 10, #4 We 10/05 Numerical differentiation: errors and effect of round-off 5.7 11 Mo 10/10 Numerical integration: idea and trapezoidal rule 5.1 12, #5 We 10/12 Numerical integration: Simpson and other rules 5.2 13 Mo 10/17 Numerical integration: Gaussian quadrature 5.3 14, #6 We 10/19 Approximation: concepts and theory 4.1-4.3 15 Mo 10/24 Approximation: orthogonal polynomials 4.4 16, #7 We 10/26 Approximation: relation to interpolation 4.5-4.7 17 Mo 10/31 Midterm exam 18, #8 We 11/02 Rootfinding: basic methods 2.0-2.3 19 Mo 11/07 Rootfinding: theory of fixed-point methods 2.5 20, #9 We 11/09 Systems of nonlinear equations: Newton's method 2.10, 2.12 21 Mo 11/14 Systems of nonlinear equations: Newton's method 2.11 22, #10 We 11/16 Numerical o.d.e.'s: problem and mathematical theory 6.1 23 Mo 11/21 Numerical o.d.e.'s: basic methods, local truncation error 6.2-6.5 24, #11 We 11/23 Numerical o.d.e.'s: accuracy and stability 6.2 25 Mo 11/28 Numerical o.d.e.'s: linear multi-step methods 6.8 26, #12 We 11/30 Numerical o.d.e.'s: Runge-Kutta methods 6.10 27 Mo 12/05 Numerical o.d.e.'s: methods for stiff problems 6.9 28, #13 We 12/07 Computer numbers: IEEE-standard for floating-point numbers 1.2 29 Mo 12/12 Computer numbers: IEEE-standard for floating-point numbers 1.2 Mo 12/19 03:30-05:30 Final Exam Note the date and time!