Course Description
Methods for finding approximate numerical solutions to a variety of mathematical problems, featuring careful error analysis. A mathematical software package will be used to implement iterative techniques for nonlinear equations, polynomial interpolation, integration, and problems in linear algebra such as matrix inversion, eigenvalues and eigenvectors.
Additional Requirements for Graduate Students:
Extra problems which are more difficult or theoretical on
homework.
Athena Title
Numerical Analysis I
Prerequisite
[(MATH 3000 or MATH 3300 or MATH 3300E or MATH 3500 or MATH 3500H) and (MATH 3100 or MATH 3100H) and (CSCI 1301-1301L or CSCI 1360 or CSCI 1360E or ENGR 1140 or ENGR 1140H or STAT 2360-2360L)] or permission of department
Semester Course Offered
Offered fall and spring
Grading System
A - F (Traditional)
Course Objectives
The student will understand the limitations of computers in representing and computing with numbers, will understand the role of error analysis and computational error in mathematics and applications. The student will learn different schemes for solving equations, computing derivatives and integrals numerically, and will understand the dual problems of speed of computation and accuracy of results.
Topical Outline
1. Representations of numbers, computational errors. 2. Taylor's Theorem and error estimates. 3. Numerical solution of equations: successive bisection, Newton's method, error estimates. 4. Polynomial interpolation (Newton, Lagrange). 5. Numerical differentiation and integration: Trapezoidal and Simpson's rules, Romberg and adaptive schemes, Gaussian quadrature, Legendre polynomials. 6. As time permits, numerical linear algebra: Vector and matrix norms, matrix factorizations, numerical solution of systems of linear equations.
Syllabus