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6341 EGM Instructor: Numerical Methods of Engineering Analysis Summer 2008 Dr. Renwei Mei, 307 Nuclear Science Building, rwmei@ufl.edu Ph. 352-392-0888 Textbook: An Introduction to Numerical Analysis, 2nd Ed by Kendall E. Atkinson Detailed Lecture Notes will be available for each chapter. COURSE CONTENTS 1. Introduction Math review (mean value theorems, Taylor series expansion) Computer Arithmetic and Errors (roundoff error, truncation error, floating point arithmetic significant digits, absolute and relative errors, error propagation) Root finding Bisection method, Newton's method, secant method, method of false position (regula falsi), successive iteration method, Muller's method, repeated roots, Brent s method Solving sets of linear equations Matrix review, norm, Gauss elimination and Gauss-Jordan method, L-U decomposition, Determinant and matrix inversion, condition number, iterative methods. Interpolation methods Method of undetermined coefficient, Lagrangian interpolation, Newton s divided difference, finite difference, error detection in data, Interpolation error, Hermite interpolation, cubic spline, least square method. Approximation of functions Weierstrass theorem, minimax approximation, least square approximation, orthogonal polynomials, Gram-Schmidt theorem, Numerical integration and differentiation Derivatives from difference tables, Newton-Cotes Integration Formulae (mid point rule, trapezoidal rule, Simpson rules), s Romberg integration, Richardson extrapolation, Gaussian quadrature, Gauss-Hermite quadrature, imperfect integral, adaptive integration, 2-d integration Numerical methods for ODE s Taylor series expansion for ODE, Euler & modified Euler methods, Runge-Kutta method and adaptive method, multi-step methods, systems of equations and highorder equations, boundary-value problems 2. 3. 4. 5. 6. 7. Grading: 30% 30% 40% Homework: A set of problems will be assigned and collected regularly. Mid-term exam. Final Exam (cumulative) at the final week of the class. LETTER GRADE: A: 90-100; C: 70-75; Academic Honesty: B+: 86-89; D+: 66-69; B: 80-85; D: 55-65; C+: 76-79; E: 0-54 All students admitted to the University of Florida have signed a statement of academic honesty committing themselves to be honest in all academic work and understanding that failure to comply with this commitment will result in disciplinary action. This statement is a reminder to uphold your obligation as a student at the University of Florida and to be honest in all work submitted and exams taken in this class and all others. Accommodations for Disabilities: Students with disabilities who are requesting classroom accommodation must first register with the Dean of Students Office. The Dean of Students Office will provide documentation to the student who must then provide this documentation to the Instructor when requesting accommodations.

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