Math 449
Numerical Applied Mathematics
Professor Wickerhauser
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NEWS:
- The Final Exam is now available. It
is due Friday, December 16th in the Math Office, room 100,
Cupples I Hall, by 3:00 PM.
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QUICK LINKS:
- Here is a nice 3-page 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.
- There is a free 1982
version of MatLab suitable for some of the homework assignments.
- 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.
- Example final exams from Math 449:
Fall 2008,
Fall 2009,
and
Fall 2010.
- Example midterm exams from Math 449:
Fall 2008,
Fall 2009,
and
Fall 2010.
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SAMPLE PROGRAMS:
- Synthetic division Matlab function syndiv.m.
- Sample code xcosx.txt to solve x=cos(x)
by fixed-point iteration and plot the result.
- Sample programs bin2dec.m and dec2bin.m to convert
between binary and decimal integer formats.
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eg-iter.txt: evaluate 20 terms of a two-term
recurrence relation.
- Sample program eulerdemo.m for Euler's method.
- 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.]
- Macsyma usage example macsyma.txt:
formulas for the first 21 Chebyshev polynomials.
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eg-plot3.txt: plot the edges of a cube.
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Corrected help for Matlab programming for Sec.2.1, algorithm 1, p.51.
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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, Math 217, and Math 309. NOTE: Students with credit for
Math 404 or 405 [last taught in 2004] 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 115.
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 9
(Solutions)
- HW #2, due Fri, Sep 16
(Solutions)
(2-1-3a.jpg)
(2-3-2.jpg)
(Graphs)
- HW #3, due Fri, Sep 24
(Solutions)
- HW #4, due Fri, Sep 31
(Solutions)
- HW #5, due Fri, Oct 7
(Solutions)
(4-5-a1.jpg)
(4-6-a1.jpg)
- HW #6, due Wed, Oct 19
(Solutions)
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- HW #7, due Fri, Oct 28
(Solutions)
- HW #8, due Fri, Nov 4
(Solutions)
- HW #9, due Fri, Nov 11
(Solutions)
- HW #10, due Fri, Nov 18
(Solutions)
(8-2-2.jpg)
- HW #11, due Fri, Dec 2
(Solutions)
- HW #12, due Fri, Dec 9
(Solutions)
(9-7a13af.jpg)
(9-7a13ar.jpg)
(9-7a13bf.jpg)
(9-7a13br.jpg)
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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. Please print and 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
Friday, October 21st, 2011. There will be one cumulative take-home final examination emphasizing the remaining
material, due on Friday, December 16th, 2011 by 3:00 pm in the
Mathematics Department Office, room 100, Cupples I Hall.
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% |
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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.
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 free 1982 version of MatLab suitable
for some of the homework assignments. A freeware
imitation of current MatLab is also available, called Octave. It does not have
the symbolic algebra functions of MatLab, but those are available within the
freeware Macsyma system.
Office Hours. Mondays, 4-5pm, or by
appointment, in Cupples I, room 105a.
Questions? Return to
M. Victor Wickerhauser's home page for contact information.
