Math 449 Numerical Applied Mathematics

NEWS:

• Homework policy change: The lowest HW will not be counted, and the homework score will instead be the average of the top 11 HW percentages.
• The final exam is now available. Please use CrowdMark to send me your solutions.

SAMPLE PROGRAMS:

• eg-iter.txt: evaluate 20 terms of a two-term recurrence relation.
• xcosx.txt: solve x=cos(x) by fixed-point iteration and plot the result.
• Corrected help with Matlab function handles in Sec.2.1, algorithm 1, p.51.
• bin2dec.m and dec2bin.m: convert between binary and decimal integer formats.
• eg-plot3.txt: plot the edges of a cube.
• syndiv.m: synthetic division Matlab function.
• macsyma.txt: formulas for the first 21 Chebyshev polynomials, Macsyma usage example.
• splineplot.txt: plot two cubic splines on 4 knots, Octave example.
• parametric.txt: plot a parametric Bezier curve, Macsyma example.
• parametric.txt: plot a Bezier curve on 4 control points, Octave example.
• eulerdemo.m: Euler's method, Octave function.
• ceuler.m: centered Euler ODE solver instability demo, Octave example.
• Function "nelder.m" as implemented in the textbook's software web site is buggy. Download a fixed nelder.m and use it instead. [Search for "CORRECTED" to find the two mistakes.]

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 217, Math 309, and CSE 131 or 200 (or other programming experience with permission of the instructor).

Time. Classes meet Mondays, Wednesdays, and Fridays, 3:00 pm to 3:50 pm, in Rudolph Hall, Room 203.

Text. The lectures will follow John H. Matthews and Kurtis D. Fink, Numerical Methods Using MATLAB, fourth edition, ISBN 0-13-065248-2, Pearson, 2004. 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 submit your solutions using CrowdMark. Problem sets will be assigned as follows:
 HW #1, due Fri, Sep 6 HW #2, due Fri, Sep 13 HW #3, due Fri, Sep 20 HW #4, due Fri, Sep 27 HW #5, due Fri, Oct 4 HW #6, due Fri, Oct 11
 HW #7, due Sun, Oct 27 HW #8, due Fri, Nov 1 HW #9, due Fri, Nov 8 HW #10, due Sun, Nov 17 HW #11, due Fri, Nov 22 HW #12, due Fri, Dec 6 (last class)
The lowest HW will not be counted, and the homework score will instead be the average of the top 11 HW percentages. Solutions must be completed by 11:01 pm 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. Please submit: (i) the program, with a comment for every line, (ii) the input you gave it, and (iii) the output it produced, for at least one example run.

Tests. There will be one midterm examination in class on Wednesday, Oct. 23rd, 2019. (2019 Midterm conditions -- same as 2016 and 2018.) There will be one cumulative take-home final examination emphasizing the remaining material, due on Thursday, December 12th, 2019 by 8:00PM. It will be presented on CrowdMark.

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:

 Course score at least: Letter grade at least: 90% 80% 70% 60% A B C D

Students taking the Cr/NCr or P/F options will need a grade of D or better to pass. Students auditing will be required to attend at least 37 of the scheduled 41 lectures. Please identify yourself to the instructor at the first class meeting.

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 a freeware alternative of MatLab, called Octave. It does not have the symbolic algebra functions of MatLab, but those are available within the freeware Macsyma system.

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