Math 449 Numerical Applied Mathematics
Professor Wickerhauser

NEWS:
 The final exam is now available.
Please use CrowdMark to send me your solutions.

QUICK LINKS:
 Chapter 8 exercises from the
4th Edition. Be careful, they are out of order, first 8.2, then
8.3, then 8.1.
 Access CrowdMark using your WUSTLConnect login at
https://app.crowdmark.com/signin/wustl
 Octave is a freeware
imitation of current MatLab. It does not have
the symbolic algebra functions of commercial MatLab.
 Download Macsyma
to help you with your symbolic calculations.
 Here is NumericalMethods7.1.zip, a
compressed archive of the MatLab codes referenced in the text.
 Article
on differentiation without taking differences.
 Here is a nice 3page online
proof that Gaussian quadrature abscissas and weights are,
respectively, roots and integrals of orthogonal polynomials.
 Some examples of cubic spline interpolation (courtesy of Prof. Sawyer):
 Some examples of Fourier series approximation (courtesy of Prof. Sawyer):
 One depiction of a rotation
matrix from xkcd.com.
 Example final exams from Math 449:
Fall 2008,
Fall 2009,
Fall 2010,
and
Fall 2011.
 Example midterm exams from previous years of Math 449:
Fall 2011, and
Fall 2016.

SAMPLE PROGRAMS:
 egiter.txt: evaluate 20 terms of a
twoterm recurrence relation.
 xcosx.txt: solve x=cos(x)
by fixedpoint 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.
 egplot3.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 0130652482,
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
(Solutions)
 HW #2, due Fri, Sep 13
(Solutions)
(Graphs)
 HW #3, due Fri, Sep 20
(Solutions)
(Graphs)
 HW #4, due Fri, Sep 27
(Solutions)
 HW #5, due Fri, Oct 4
(Solutions)
 HW #6, due Fri, Oct 11
(Solutions)


 HW #7, due Sun, Oct 27
(Solutions)
 HW #8, due Fri, Nov 1
(Solutions)
 HW #9, due Fri, Nov 8
(Solutions)
 HW #10, due Sun, Nov 17
(Solutions)
 HW #11, due Fri, Nov 22
(Solutions)
 HW #12, due Fri, Dec 6 (last class)



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, welldocumented 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
takehome 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:  90%  80%  70%  60% 
Letter grade at least:  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, 45pm, or by
appointment, in Cupples I, room 105a.
Questions? Return to
M. Victor Wickerhauser's home page for contact information.