Date: June 5th.
Meet in 270 Korman 11:50-11:55A.M.
Room: to be determined.
What to know: material covered by May 31 (test1 + test2 + 1 lecture).
Format: two-hour test, 6-8 questions with parts (some true/false + midterm-type questions).
You are allowed to use a one-sided sheet with formulas and theorem statements.
Focus: homework, examples (textbook, class), midterms, samples, quizzes.
Office hours: by appointment.
Important topics:
1. Taylor polynomials.
2. Error terms in Taylor's approximation.
3. Polynomial evaluation (operations count).
4. Decimal and binary arithmetic.
5. Floating-point numbers.
6. Absolute and relative errors.
7. Under/overflow, noise in evaluation.
8. Significant digits, loss of significance.
9. Bisection method (error analysis).
10. Newton's method (error analysis).
11. Secant method (error analysis).
12. Fixed point iterations.
13. Aitken's formula.
14. Lagrange interpolation formula.
15. Divided differences.
16. Newton interpolation formula.
17. Error in polynomial interpolation.
18. Minimax problem and Chebyshev polynomials.
19. Splines (including linear and cubic).
20. Least squares approximation and Legendre polynomials.
21. Numerical integration (+ error estimates).
22. Gaussian quadrature.
23. Numerical differentiation (+ method of undetermined coefficients).
24. Linear systems, Gaussian elimination.