Supplementary Notes to Math 551Numerical
Methods, Spring 2013
Tom DeLillo, WSU Math Dept.
May 9, 2013
1
Introductory remarksLecture 1/22/13
I will try to maintain here a record of my lectures, with varying levels of
detail, as a supplement to our text [CM]. This is not meant to replace or
completely reproduce the lectures. Please let me know if you spot any typos
or errors. I will also post pdf files of older notes when necessary and type
them up here in this latex file as frequently as I can manage. (Students who
want to learn latex, can volunteer to help! I will send you the latex file as
a sample to help you get started.)
A good supplement to our text is the
book [CVL]. It contains some more detailed derivations and some analysis
(one theorem per chapter) of the many of the methods we will be discussing.
Some of my notes here and in class will follow [CVL]. Another text to be
aware of in [TB] which we use frequently in our Math 751, Numerical Linear
Algebra course offered each Fall. I will adopt the idea there of introducing
the singular value decomposition almost immediately, since it sheds so much
light on the properties of matrices and linear systems
Ax
=
b
which will be
an ongoing concern to us.
A glance at the table of contents of our text [CM] will show you that
this course will probably draw from every undergraduate math course that
you have taken from calculus to differential equations to linear algebra. The
point of this course is to develop efficient, accurate, and reliable methods for
computing numerical solutions to many of the problems you have discussed
in your core mathematics courses. You will need access to MATLAB and are
advised to get the
Student Edition of MATLAB
.
1
Table 1: Approximate syllabus
Week
Tuesday lecture
Thursday lecture
1
Sec. 1.7
difference quotient error
2
lin. alg. rev.: Sec. 2.9 norms
. . . , matrix norms, Sec. 10.1 SVD
3
SVD cont.
SVD, oper. counts
4
oper. counts, start Chap. 2
Chap. 2...
5
lutx, bslashtx, oper. counts
det(
A
)
, A

1
6
tridisolve
sec. 3.1poly. interp.
7
3.2,3.3 pw cubic, spline
3.4, 3.5 spline, periodic
8
finish Chap 3
4.1,4.2, Newton, Picard iter.
9
4.3,4.4 secant
Exam I thru 4.4
10
11
12
13
14
15
I’ll include here some short, unpolished pieces of MATLAB code to il
lustrate the discussion.
I’ll try to make these available on my web page
eventually, but many of them are short enough that you can just type them
in yourself.
Numerical methods, along with theory and experiment, are fundamen
tal to modern applied science and engineering. For an incisive overview of
the field of numerical analysis, read Nick Trefethen’s essay in the Appendix
of [TB] on
The Definition of Numerical Analysis
or on his web site [LNT]—
read it now and at the conclusion of this course.
For those of you who
consider yourselves to be pure mathematicians, you might take the attitude
that you don’t fully understand a topic unless you know how to compute
effectively!
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 Spring '13
 TomDeLillo
 Math, Linear Algebra, matlab, ax