### http://interval.louisiana.edu/courses/455/spring-2005-math-455-outline.html Math. 455, Spring, 2005 Course Outline

Instructor: R. Baker Kearfott, Department of Mathematics, University of Louisiana at Lafayette
Office hours and telephone, Email: rbk@louisiana.edu.

This outline is a tentative guide. Problems will be assigned as the topics are covered, and will usually be due on Friday three periods after the day they are assigned. Where no section from the text book is listed, the lecture will come from supplementary material. This outline is subject to some change.
`         Day Section and Description          1. 1.1, 1.2 -- Review of calculus		  1.3 -- Computer arithmetic          2. 1.4      -- Roundoff error                         Interval analysis          3.          -- Introduction to Matlab             1.5         Computer software sources			 (in-class demo)          4. ---         FIRST EXAM              ---------------------          5. 2.1, 2.2 -- The method of bisection             2.3, 2.4 -- The secant method and Newton's method          6. 2.5      -- Error analysis                         Interval Newton methods          7. 2.6 and  -- Software             supplement          8. ---         SECOND EXAM        --------------------------          9. 3.1         Review of Taylor polynomials                         Interval enclosures         10. 3.2      -- Lagrange interpolation             3.4      -- Hermite interpolation         11. 3.3      -- Divided differences         12. 3.5      -- Spline interpolation             3.6      -- Parametric curves         13. ---         THIRD EXAM         --------------------------         14.          -- Review of the definition of integral             4.2      -- Basic quadrature rules         15. 4.3      -- Composite quadrature             4.4      -- Gaussian quadrature         16. 4.6      -- Adaptive quadrature                      -- Interval adaptive quadrature         17. 4.9         numerical differentiation                         automatic differentiation         18. ---         FOURTH EXAM        --------------------------         19. 5.1 and  -- Introduction to initial value problems             supplement         20. 5.2, 5.3 -- Taylor methods and Runge-Kutta methods             5.4      -- Predictor-corrector methods         21. 5.6      -- Adaptive techniques             5.7      -- Methods for systems of equations         22. 5.8      -- Stiff differential equations         23. 5.9      -- Survey of software         24. 6.1, 6.2 -- Linear systems of equations and             6.3      -- Pivoting strategies         25. ---         FIFTH EXAM         --------------------------         26. 6.4      -- Linear algebra             6.6      -- Techniques for special matrices         27. 6.7      -- Survey of software         28.             Review`