MW 4-5:50, Randell 238B.
Instructor: Anatolii Grinshpan
Office hours: Tue, Thu 4-5 (Korman 247) or by appointment.
Sept 22. Introduction to the course.
Sept 29. Nested multiplication and long division. Approximation of irrational numbers.
Oct 6. Babylonian numerals. Octal and hexadecimal systems. Error, absolute and relative error. Significant digits.
A&H notes: 2.2
Oct 8. Quiz 2 (binary/denary arithmetic, polynomial evaluation). Error classification.
Oct 13. No class: Columbus day.
Oct 15. Propagation of error in arithmetic operations. Noise in evaluation. Underflow/overflow.
Oct 20. Subnormal numbers and biased exponents. Single (32-bit), double (64-bit), and extended (80-bit) precision models.
Oct 22. Quiz 3 (error arithmetic, floating-point format). Discussion. Practice test. Week 4 answers. Homework 5: none.
Oct 27. Midterm 1 (lectures of Sept 22 – Oct 22, homework, exercises, quizzes). Answers. Extra credit: Kahan’s algorithm.
Oct 29. Iterations
and rootfinding. Rate and
order of convergence. Bisection and
Nov 3. Midterm
1 discussion. Examples on
Handout: a chaotic search for i (hardcopy). A&H notes: 3.3. Week 6 answers.
Nov 10. Quiz 4 (rootfinding). Fixed point iterations.
Nov 12. Behavior of fixed point iterates. Types of fixed points. Contractive mapping theorem: proof.
Examples. Week 7 exercises.
Nov 17. Quiz 5 (fixed point iterations). Aitken’s extrapolation formula. Logistic map. An example.
Week 7 answers. Week 8 exercises. Homework 8: none.
Nov 19. Logistic map (continued). Stability of roots. Wilkinson’s example.
Nov 24. Midterm 2 (lectures of Oct 29 – Nov 19, homework, exercises, quizzes). Answers. Problem 3B. Problem 4B.
Dec 1. Lagrange and
Dec 3. The minimax problem. Chebyshev polynomials.
Dec 5. Office hours 2-3 P.M., Korman 255.
Dec 9. Office hours: 12-2 P.M., Korman 247. Practice exam. Answers.
Dec 10. Office hours: 1:30-2:15 P.M. Korman 255. Answers to exercises. Graphs.
Dec 11. Office hours: 1-2 P.M., Korman 255.
Dec 12. Final exam (all lectures, homework, quizzes, exercises): 8-10 A.M., Randell 231.
Answers. Problem 6.