Text: Epperson, An Introduction to Numerical Methods and Analysis , Wiley (2002)

Tentative Course Outline:

Week 1: Chapter 1, Calculus Review, Error and Numerical Computing.

Weeks 2 and 3: Chapter 2, Survey of Simple Methods and Tools.

Weeks 4 and 5: Chapter 3, Root Finding for Nonlinear Equations -- Bisection, Newton's Method, Secant Method, Fixed Point Iteration, Convergence Issues.

Week 6: Chapter 4, Interpolation and Approximation -- Lagrange Polynomials, Divided differences, Cubic spines

Week 7: Midterm Exam

Weeks 8 and 9: Chapters 4 and 5, Interpolation and Approximation and Integration -- Review Cubic spines, Least squares, Review numerical differentation, Trapezoidal, Simpson, Midpoint methods and Richarson extrapolation and Romberg integration

Weeks 10-12: Chapter 6 -- Ordinary Differential Equations - Initial value problems -- Euler's Method, and Taylor Series Methods and Consistency. Runge-Kutta Methods and Multi-step Methods, Higher Order Systems. Linear Systems of ODES, Stability with respect to step size, Stability with respect to round-off, Stiff ODEs.

Weeks 13-14: Chapter 7 -- Numerical Linear Algebra - Gaussian Elimination, Partial pivoting, Back-substitution, LU-decomposition, Determinants, Matrix Inverse, Storage, Error growth, Tri-diagonal matrices. Norms, Error analysis, Condition number, Iterative Methods Nonlinear Systems

Week 15: Project Presentations and Final Exam

Grading: (Regular) Homework and Class Participation 20%, Midterm Exams 25%, Final Exam 35%, Project 20%.   Make-up exams may be allowed if discussed with me prior to exam date.   Project is due November 28 -- 10% off for each day late. Project must be approved by professor by November 1.


Project Ideas and Information