Math. 455 Course Outline
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.
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Day Section and Description
1. 1.1, 1.2 -- Review of calculus
2. 1.3, 1.4 -- Computer arithmetic and roundoff error
3. Interval analysis
4. Fortran 90 and USL's UCS system
5. 1.5 -- Computer software sources
6. --- FIRST EXAM ---------------------
7. 2.1, 2.2 -- The method of bisection
8. 2.3, 2.4 -- The secant method and Newton's method
9. 2.5 -- Error analysis
10. Interval Newton methods
11. 2.6 and -- Software
supplement
12. --- SECOND EXAM --------------------------
13. Review of Taylor polynomials
14. Interval enclosures
15. 3.2 -- Lagrange interpolation
16. 3.4 -- Hermite interpolation
17. 3.5 -- Spline interpolation
18. 3.6 -- Parametric curves
19. --- THIRD EXAM --------------------------
20. -- Review of the definition of integral
4.2 -- Basic quadrature rules
21. 4.3 -- Composite quadrature
22. 4.4 -- Gaussian quadrature
23. 4.6 -- Adaptive quadrature
24. -- Interval adaptive quadrature
25. 4.9 numerical differentiation
26. automatic differentiation
27. --- FOURTH EXAM --------------------------
28. 5.1 and -- Introduction to initial value problems
supplement
29. 5.2, 5.3 -- Taylor methods and Runge-Kutta methods
30. 5.4 -- Predictor-corrector methods
31. 5.6 -- Adaptive techniques
32. 5.7 -- Methods for systems of equations
33. 5.8 -- Stiff differential equations
34. 5.9 -- Survey of software
35. 6.1, 6.2 -- Linear systems of equations and
Gaussian elimination
36. 6.3 -- Pivoting strategies
37. 6.4 -- Linear algebra
38. 6.6 -- Techniques for special matrices
39. 6.7 -- Survey of software
40. --- FIFTH EXAM --------------------------
41. Review
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