T 12-1:50, room 412 Matheson, R 12-1:50, room 105D Korman.
Instructor: Anatolii Grinshpan
Current office hours: TR 3:30-5 or
by appointment, 270 Korman
Course information. Math resource center. Academic Calendar.
Textbook supplements (Atkinson’s website).
MATLAB tutorial. Numerical Computing with MATLAB (Moler’s book).
Outline
Apr 3. Introduction. Taylor polynomials.
Apr 5. Basics of MATLAB. Polynomial evaluation.
Approximation by
Problems: 2 a), 4, 14 (1.1), 1, 4, 9 a), 13 (1.2), 7 (1.3).
Apr 10. Decimal and binary number systems. Floating-point numbers.
Discussion
of IEEE (Goldberg’s paper).
Apr 12. Quiz: decimal and binary arithmetic (appendix E, problems on page 531).
LAB: error arithmetic. Extra credit.
Apr 17. Rootfinding.
Problems 1 a), d), g), 11 (3.1), 2 a), d), 3, 13 (3.2).
Apr 19. Quiz: bisection and
LAB: rootfinding. Example from class.
Strang’s
paper on Newton’s method and iterations.
Apr 24. Secant method. Fixed point iterations.
Problems: 8 (3.3), 3-7 (3.4)
Apr 26. LAB: fixed point iterations, ill-behaving rootfinding.
Examples: multiple root slow down (newton1, newton2),
root instability for polynomials (wilkin).
May 1. Quiz: fixed point iterations.
Polynomial interpolation. Review.
May 3. Test 1: Chapters 1-3. Important topics.
Focus: homework and quiz questions, in class examples.
May 8. Lagrange
and
Problems: 3, 4, 7, 12, 20, 24 (4.1).
May 10. Error in polynomial interpolation. Minimax problem.
Chebyshev polynomials.
Animations for Chebyshev interpolation (by John Mathews).
Problems: 2, 9 (4.2).
May 15. Quiz: Lagrange and
Splines. Legendre polynomials. Least squares approximation.
Problems: Example 4.3.1; 2, 5 (4.5); Example 4.7.1; check formula (4.118) for i, j=0, 1, 2, 3.
May 17. Spline interpolation, Legendre polynomials. Legendre nodes.
Applet: natural cubic splines (by Tim Lambert).
Least squares approximation (continued).
Problems: 2 (4.7).
May 22. Quiz: least squares approximation.
Numerical integration, error formulas.
Gaussian quadrature.
Problems: 6, 8 (5.3).
May 24.
Review.
Problems: 6, 8, 10 (5.4).
May 29. Test 2: Chapters 4 & 5. Important topics. Sample. Sample test answers.
Focus: homework, examples (textbook, class), quizzes. Test 2 answers.
May 31. Linear systems, Gaussian elimination.
Lab: Legendre nodes, natural cubic spline.
June 5. Solving systems of linear equations: LU factorization.
Early final for graduating seniors.
Problems: Gaussian elimination, LU factorization for 3x3 systems (try your own examples).
June 7. Quiz: Gaussian elimination, LU factorization.
Solving linear systems: stability, error analysis.
Iteration methods (Jacobi and Gauss-Seidel).
Problems: 4-6 (6.5), 3, 5 (do several iteration steps by hand) (6.6).
June 12. Questions session 3:30-5 (office).
June 14. Final exam: 8-10 A.M., Matheson 307.