Applied Mathematics and Computational Science
Algebraic Techniques II
Faculty: Jerry L. Kazdan
Telephone: (215) 8985109
email: kazdan AT math . upenn . edu
Office Hours: by appointment in DRL 4E15

Topics:
The first (and primary) topic of the course is Numerical Linear
Algebra. Although we presume that everyone already knows the
basic theory, during the first few weeks will review the basics.
As a guide, after a few weeks you should be able to do most of these
AMCS 602 Linear Algebra Problems.
MATLAB is currently the best software for general scientific
numerical computations. It is wise to learn how to use this
effectively as soon as possible. Some references are listed below.
You can buy a less expensive
Student Version.
Texts and References:
 Numerical Linear Algebra by Lloyd Trefethen and David Bau
III, SIAM 1997
 Numerical Methods by Germund Dahlquist and Ake Bjorck,
Dover (reprinted from the 1974 edition). There is also a recent two volume
edition version published by SIAM.
 "Pitfalls in Computation, or why a Math Book isn't Enough,
by George E. Forsythe, Amer. Math. Monthly, 77 Oct., 1970,
pp. 931956. URL:
Forsythe, "Pitfalls in Computation"
 Matrix Computations (3rd edition) by Gene H. Gulub and
Charles F. Van Loan, Johns Hopkins Univ. Press, 1996.
 MATLAB references:
MATLAB Tutorial (Mathworks),
General,
primer,
Gockenbach Intro,
Sigmon Primer,
MIT MATLAB Tutorial,
O'Sullivan Primer
 A Special Tridiagonal Matrix
Suggested Homework (these will not be collected).
 Homework Set 1:
Problems #4, 6, 8, 9, 11, 15, 19, 20, 22, 26, 28, 30, 31, 32, 36, 40 from
AMCS 602 Linear Algebra Problems.
Lots of problems  but most of them are very short.
 Homework Set 2:
Problems #42, 43, 45, 48, 50, 51, 52, 53, 56, 58, 59, 64, 65, 66 from
AMCS 602 Linear Algebra Problems.
 Homework Set 3:
Problems #78, 79, 82, 83, 84, 85, 86, 88, 89, 94, 97, 103, 110, 119,
133 from AMCS 602 Linear Algebra Problems.
From TrefethenBau: p. 3031 #4.1, 4.2, 4.3 and p. 37 # 5.1, 5.3
 Homework Set 4:
Experiment with using SVD (and Matlab) with images. Here are
two pieces from courses elsewhere:
SVD Graphics (Sandberg) and
SVD  Graphics (AbrahamsenRichards).
The following images may be useful to play with:
Lincoln Osama.