APMA 507 - Spring 2007 - Tentative course outline

All section numbers refer to R. L. Burden and J. D. Faires "Numerical Analysis", 8th edition.

Wednesday January 17Sections 1.1 Review of Calculus
Monday January 22Sections 1.2 & 1.3Round-off errors and computer Arithmetic & Algorithms and Convergence
Wednesday January 24Sections 1.3 & 2.1Algorithms and Convergence & The Bisection Method
Monday January 29Sections 2.2 & 2.3Fixed Point Iteration & Newton's Method
Wednesday January 31Sections 2.3 & 2.4Newton's Method & Error Analysis for Iterative Methods
Monday February 5Sections 2.4 & 2.5Error Analysis for Iterative Methods & Accelerating Convergence
Wednesday February 7Section 2.6Zeros of Polynomials and Muller's Method
Monday February 12Section 3.1Interpolation and the Lagrange Polynomial
Wednessday February 14Section 3.1 Interpolation and the Lagrange Polynomial
Monday February 19Sections 3.2Divided Differences


Wednesday, February 21st, Prelim I (3:30 - 4:45 p.m.)

Monday February 26Section 3.3Hermite Interpolation
Wednesday February 28Section 3.4Cubic Spline Interpolation
Monday March 5-Spring Break
Wednesday March 7-Spring Break
Monday March 12Section 4.1Numerical Differentiation
Wednesday March 14Sections 4.2Richardson's Extrapolation
Monday March 19Section 4.3 & 4.4Elements of Numerical Integration & Composite Numerical Integration
Wednesday March 21Sections 4.5 & 4.6Romberg Integration & Adaptive Quadrature Methods
Monday March 26Section 4.7Gaussian Quadrature


Wednesday, March 28, Prelim II (3:30 - 4:45 p.m.)

Monday April 2Sections 5.1 & 5.2The Elementary Theory of Initial-Value Problems & Euler's Method
Wednesday April 4Sections 5.3 Higher Order Taylor Methods
Monday April 9Section 5.4Runge-Kutta Methods
Wednesday April 11Section 5.5Error Control and the RKF Method
Monday April 16Section 5.6Multisteps Methods
Wednesday April 18Section 5.10Stability
Monday April 23Section 6.3Numerical Analysis - What for?


Wednesday, April 25, Prelim III (3:30 - 4:45 p.m.)