640:373 Numerical Analysis I
Approximate Course Syllabus: Fall, 2008
Solution of Equations in One Variable
Lecture 1. Calculus Review (1.1) 9/02/08 (T)
Lecture 2. Bisection, False Position, Secant, Newton Methods
(2.1, 2.3) 9/04/08 (Th)
Lecture 3 Newton's method for systems, fixed point iteration,
(2.2, 10.2) 9/09/08 (T)
Lecture 4. Local Convergence, order of convergence,
(2.4) 9/11/08 (Th)
Interpolation and Polynomial Approximation
Lecture 5. Lagrange Polynomial (3.1) 9/16/08 (T)
Lecture 6. Divided Differences, Newton polynomial (3.2) 9/18/08 (Th)
Lecture 7. Hermite Interpolation (3.3) 9/23/08 (T)
Lecture 8. Piecewise Polynomial Approximation (notes) 9/25/08 (Th)
Lecture 9. Cubic Spline Approximation (3.4) 9/30/08 (T)
Lecture 10. Bezier curves (3.5) 10/02/08 (Th)
Numerical Differentiation and Integration
Lecture 11. Exam 1 10/07/08 (T)
Lecture 12. Numerical Differentiation (4.1) 10/09/08 (Th)
Lecture 13. Basic Numerical Integration Rules (4.3) 10/14/08 (T)
Lecture 14. Composite Numerical Integration (4.4) 10/16/08 (Th)
Lecture 15. Romberg Integration (4.2, 4.5) 10/21/08 (T)
Lecture 16. Gaussian Quadrature (4.7) 10/23/08 (Th)
Lecture 17. Adaptive Quadrature (4.6) 10/28/07 (T)
Initial Value Problems for Ordinary Differential Equations
Lecture 18. Theory of Initial Value Problems (5.1),
Euler's Method (5.2) 10/30/08 (Th)
Lecture 19. Taylor Methods (5.3) 11/04/08 (T)
Lecture 20. Runge-Kutta Methods (5.4) 11/06/08 (Th)
Lecture 21. Error Control (5.5) 11/11/08 (T)
Lecture 22. Exam 2 11/13/08 (Th)
Lecture 23. Multistep Methods: Derivation (5.6,5.7) 11/18/08 (T)
Lecture 24. Multistep Methods: order, consistency, local
truncation error (5.6,5.7) 11/20/08 (Th)
Lecture 25. Convergence of Multistep Methods (5.10) 11/25/08 (Tu)
Thanksgiving 11/27/08 (Th)
Lecture 26. Stability of Multistep Methods (5.10) 12/02/08 (T)
Lecture 27. Predictor-Corrector methods and
generalizations to systems (5.7,5.9) 12/04/08 (Th)
Lecture 28. Catch up and Review 12/09/08 (T)