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.
Day Section and Description
1. 1.1, 1.2 -- Review of calculus
1.3 -- Computer arithmetic
2. 1.4 -- Roundoff error
Interval analysis
3. -- Fortran 90 and USL's UCS system
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. 3.5 -- Spline interpolation
13.6 -- Parametric curves
12. --- THIRD EXAM --------------------------
13. -- Review of the definition of integral
4.2 -- Basic quadrature rules
14. 4.3 -- Composite quadrature
4.4 -- Gaussian quadrature
15. 4.6 -- Adaptive quadrature
-- Interval adaptive quadrature
16. 4.9 numerical differentiation
automatic differentiation
17. --- FOURTH EXAM --------------------------
18. 5.1 and -- Introduction to initial value problems
supplement
19. 5.2, 5.3 -- Taylor methods and Runge-Kutta methods
5.4 -- Predictor-corrector methods
20. 5.6 -- Adaptive techniques
5.7 -- Methods for systems of equations
21. 5.8 -- Stiff differential equations
22. 5.9 -- Survey of software
23. 6.1, 6.2 -- Linear systems of equations and
6.3 -- Pivoting strategies
24. --- FIFTH EXAM --------------------------
25. 6.4 -- Linear algebra
6.6 -- Techniques for special matrices
26. 6.7 -- Survey of software
27. Review