Syllabus

Topics. Computer arithmetic, error propagation, condition number and stability; mathematical modeling, approximation and convergence; roots of functions; calculus of finite differences; implicit and explicit methods for initial and boundary value problems; numerical integration; numerical solution of linear systems, matrix equations, and eigensystems; Fourier transforms; optimization. Various software packages are introduced and used.

Prerequisites. Math 1201 or equivalent programming experience, 217, and 309. NOTE: Students with credit for Math 404 or 405 cannot also receive credit for 449.

Time. Classes meet Mondays, Wednesdays, and Fridays, 3:00 pm to 4:00 pm, in Cupples I Hall, Room 207.

Text. The lectures will follow John H. Matthews and Kurtis D. Fink, Numerical Methods Using MATLAB, fourth edition, ISBN 0-13-065248-2, Prentice Hall, 2003. Note: except for Chapters 5 and 8, the fourth edition is virtually identical to the third edition.

Homework. You are encouraged to collaborate on homework, and to work additional exercises from the indicated problem sections, although the homework grade will be based only on the exercises listed below. Please return your solutions to the instructor by the end of class. Problem sets will be assigned as follows:

HW #1, due Fri, Sep 4 (Solutions) HW #2, due Fri, Sep 11 (Solutions) (Graph for 2.1, Ex.3a) HW #3, due Fri, Sep 18 (Solutions) HW #4, due Fri, Sep 25 (Solutions) HW #5, due Fri, Oct 2 (Solutions) HW #6, due Fri, Oct 9 (Solutions) (Graphs: 5-3-a5.pdf, 5-5-a2a.pdf, 5-5-a2b.pdf, 5-5-a2c.pdf)	HW #7, due Fri, Oct 23 (Solutions) HW #8, due Fri, Oct 30 (Solutions) HW #9, due Fri, Nov 6 (Solutions) HW #10, due Fri, Nov 13 HW #11, due Fri, Nov 20 HW #12, due Fri, Dec 4

Solutions are due at the end of class on the due date. Late homework will not be accepted. The problems will often require a complete proof. The homework will be judged for correctness and clarity. When the problem requires a computed solution, it must be accompanied by a correct, well-documented computer program which will be judged for its understandability.

Tests. There will be one midterm examination (Solutions) in class on Wednesday, October 14th, 2009. There will be one cumulative final examination emphasizing the remaining material on Friday December 11th, 2009 from 6:00 pm to 8:00 pm, also in the classroom.

Grading. One score will be assigned for homework, one for the midterm examination, and one for the final examination. These three will contribute in respective shares of HW 50%, MT 20%, and FE 30% to the course score. Letter grades, computed from the course score class average and standard deviation, will be at least the following:

Computing. Students are encouraged to use MATLAB and the computers available in the Arts and Sciences Computing Center for both symbolic and numerical computations. There is also a free 1982 version of MatLab suitable for most of the homework assignments.

Office Hours. Mondays and Wednesdays, 4-5pm, or by appointment, in Cupples I, room 105a.