Date: June 14
Time: 8-10 A.M.
Room: 307 Matheson.
What to know: test1 material + test2 material + last 3 lectures.
Format: two-hour test, 6-8 questions with parts (some true/false + midterm-type questions).
You can use a one-sided sheet with formulas and theorem statements.
Focus: homework, examples (textbook, class), midterms, samples, quizzes.
There will not be any unfamiliar types of questions.
Office hours: Tuesday, Thursday 3:30-5 or 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.
25. LU factorization.
26. Error analysis for Ax=b, condition number.
27. Iterations for solving Ax=b (Jacobi and Gauss-Seidel methods).