WF 12-1:50, Curtis 452.
Instructor: Anatolii Grinshpan
Office hours: M 2-3, W 3-5 (Korman 247) or by appointment.
Apr 1. Introduction to the course. Number systems: decimal and binary arithmetic.
Apr 3. More on binary arithmetic. Octal, hexadecimal, Mayan, and Babylonian systems.
A & H notes: 2.2
Apr 8. Quiz 1 (denary and binary arithmetic). More on errors. Approximation of irrational numbers.
Apr 10. Propagation of error in function evaluation and arithmetic operations.
A & H notes: 2.3.
Apr 15. Four modes of rounding. Polynomial evaluation and operation count. Nested multiplication.
Apr 17. Quiz 2 (error arithmetic and propagation). Fixed-point and floating-point representations of numbers.
A & H notes: 2.1.
Apr 24. Quiz 3 (IEEE format). Correctly rounded operations. Rounding estimates. Summation.
Apr 29. Week 3 answers. Midterm 1 (lectures of April 1 – April 24).
Extra credit: Kahan’s algorithm, plot the absolute relative error of the IEEE floating-point representation (single or double precision).
May 1. Exam discussion. Taylor polynomials.
A & H notes: 1.1
May 6. Taylor polynomials. Error sequences: order and rate.
May 8. Quiz 4 (Taylor polynomials). Rootfinding. Bisection.
A & H notes: 3.1.
May 13. Week 6 answers. Newton’s method.
May 15. Division via Newton’s iteration. Stability of roots.
A & H notes: 3.5.
May 20. Quiz 5 (Bisection and Newton’s method). Secant method.
May 22. The order and rate of the secant method. Homework discussion.
May 27. Midterm2 (lectures of May 1 – May 22).
May 29. Fixed-point iteration. The contraction mapping theorem.
June 5. Newton interpolation and interpolation error. The minimax problem.
Office hours: June 8, 2-3 (Korman 247), 3-4+ (Korman 253).
June 10. Final Exam (all lectures), 1-3 P.M., Curtis 451. Answers.