Instructor: Anatolii Grinshpan
Office hours: TWR 4-6, Korman 247, or by appointment.
Apr 6. Octal and hexadecimal systems. Babylonian and Mayan numerals.
Apr 11. Propagation of error in arithmetic. Examples. Error in function evaluation.
A & H: Propagation of error.
Apr 13. Quiz 1 (number systems and conversion). Mean-value theorem.
A & H: Polynomial evaluation. Nested multiplication and operation count.
Apr 25. Computer arithmetic. Examples. The relative error of floating-point representation.
Apr 27. Midterm I (lectures of April 4 – April 25).
May 4. Taylor polynomials (continued). Irrationality of e.
A & H: Calculation of functions.
May 9. Computing derivatives and integrals via Taylor polynomials.
A & H: Rootfinding.
May 11. Quiz 3 (Taylor approximation). Newton’s method. Examples and error analysis.
Division via Newton’s iteration. A & H: Rootfinding (continued).
Secant method: error analysis. When to stop an iteration.
May 18. Quiz 4 (Bisection and Newton’s method). Multiple root. Stability of roots.
Fixed-point iteration. A & H: Multiple roots. Perturbation analysis.
May 25. Midterm II (lectures of May 2 – May 23).
May 30. Bit shifting and the logistic map. Lagrange interpolation formula.
A & H: Interpolation.
Jun 1. Divided differences and polynomial interpolation. Interpolation error. The minimax problem.
June 6. Quiz 5 (Lagrange interpolation, divided differences). Newton interpolation formula. Chebyshev’s theorem.
June 8. Applications to numerical differentiation and integration.
Jun 13. Final Exam (all lectures): 10:30-12:30 Drexel Plaza GL 20.