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Title: Math/Publications/Online Texts - Linear Algebra and Applications Textbook by Thomas Shores. GIFs of pages.
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Linear Algebra and Applications Textbook
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Linear Algebra and Applications Textbook
Welcome again. In order to enable prospective users to
preview my text easily and conveniently, in the past I have put a
copy of it on the web for your perusal. In the last few years I've received many helpful comments and appreciative notes for having done so. I would like to thank those of you who sent me these notes and comments. You have helped me substantially improve the text. I am now under contract with Springer-Verlag and the book has been published in their Undergraduate Texts in Mathematics series in hardbound and, more recently, soft cover editions. Therefore, I have removed the on-line copy. I will leave the table of contents below for informational purposes, along with errata sheets for the each version of the textbook. A few comments:
Why this text? I'm committed to a balanced blend of
theory, application and computation. Mathematicians are
beginning to see their discipline as more of an
experimental science, with computer software as the
"laboratory" for mathematical experimentation. I believe
that the teaching of linear algebra should incorporate
this new perspective. My own experience ranges from pure
mathematician (my first research was in group and ring
theory) to numerical analyst (my current speciality).
I've seen linear algebra from many viewpoints and I think
they all have something to offer. My computational
experience makes me like the use of technology in the
course -- a natural fit for linear algebra -- and
computer exercises and group projects also fit very well
into the context of linear algebra. My applied math
background colors my choice and emphasis of applications
and topics. At the same time, I have a traditionalist
streak that expects a text to be rigorous, correct and
complete. After all, linear algebra also serves as a
bridge course between lower and higher level
mathematics.
If you have any suggestions or comments, drop me a line. I appreciate any
feedback.
Resources
A complete solutions manual to all exercises and problems in the text is available to instructors who have adopted the text. Instructors who would like a copy of this manual should contact Mark Spencer via email to Mark.Spencer@springer.com.
For the benefit of instructors and students using my text, I'm moving a number of downloadable files on my website that pertain specifically to the text into their own directories. I also have complete solution keys to the exams and projects that are found in the directories below. I will email these to instructors who are using my text upon request. The text materials come in three flavors: pdf for perusal, lyx and tex for modification and use by instructors.
Maple
Notebooks Tutorial notebooks in Maple, some of
which are the basis for linear algebra projects.
Mathematica
Notebooks Tutorial notebooks in Mathematica, some
of which are the basis for linear algebra projects (in
old Mathematica .ma and new .nb formats. I'll update them at a future date, since I haven't used Mathematica in a while.)
Matlab Files Program files for Matlab and a Matlab-like program called Octave which I have found
very useful in linear algebra.
Sample
Documents Here are sample syllabi and class policy statements which I have used with my text. Formats are html, tex and lyx.
Sample
Exams and Projects Here are sample exams which I have used along
with my text; there are latex and lyx files, so instructors
may massage them to suit their own needs.
Errata Sheets
It's frustrating to debug a text that you've written youself. I've discovered that far too often I was reading what I thought should be on the page rather than what actually on the page. I want to thank my many students and colleagues who tracked down many of the errata in the text. I've also learned that editorial help can turn up most unexpectedly. I owe a special debt of gratitude to Dr. David Taylor and Dr. Mats Desaix, who read a good deal of the text very carefully entirely at their own initiative, and brought a good number of errors to my attention. Somehow, I suspect the battle is not done, so if you find any errors not listed below, please report them to me.
The errata for the soft cover printing of the text apply also to the hardbound printing, which came out six month earlier than the soft cover text. Conversely, the errata for the hardbound printing were excised in the soft cover printing. While writing the instructors' solution manual, I rechecked all the solutions to exercises in the back of the text and found some more errors, which are recorded below in the soft cover errata
Errata sheet for soft cover text
Additional errata sheet for hardbound text
Here is the table of contents of the text:
Applied Linear Algebra and Matrix Analysis
by
Thomas S. Shores
Copyright © 2007 Springer Science+Business Media, LLC
Preface
Chapter 1. LINEAR SYSTEMS OF EQUATIONS
1. Some Examples
2. Notations and a Review of Numbers
3. Gaussian Elimination: Basic Ideas
4. Gaussian Elimination: General Procedure
5. *Computational Notes and Projects
Chapter 2. MATRIX ALGEBRA
1. Matrix Addition and Scalar Multiplication
2. Matrix Multiplication
3. Applications of Matrix Arithmetic
4. Special Matrices and Transposes
5. Matrix Inverses
6. Basic Properties of Determinants
7. *Computational Notes and Projects
Chapter 3. VECTOR SPACES
1. Definitions and Basic Concepts
2. Subspaces
3. Linear Combinations
4. Subspaces Associated with Matrices and Operators
5. Bases and Dimension
6. Linear Systems Revisited
7. *Computational Notes and Projects
Chapter 4. GEOMETRICAL ASPECTS OF STANDARD
SPACES
1. Standard Norm and Inner Product
2. Applications of Norm and Inner Product
3. Orthogonal and Unitary Matrices
4. *Change of Basis and Linear Operators
5. *Computational Notes and Projects
Chapter 5. THE EIGENVALUE PROBLEM
1. Definitions and Basic Properties
2. Similarity and Diagonalization
3. Applications to Discrete Dynamical Systems
4. Orthogonal Diagonalization
5. *Schur Form and Applications
6. *The Singular Value Decomposition
7. *Computational Notes and Projects
Chapter 6. GEOMETRICAL ASPECTS OF ABSTRACT
SPACES
1. Normed Spaces
2. Inner Product Spaces
3. Gram-Schmidt Algorithm
4. Linear Systems Revisited
5. *Operator Norms
6. *Computational Notes and Projects
Table of Symbols
Answers to Selected Exercises
References
Index
[ T O P ] [ H O M E ] [ |
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Textbook | by | Thomas | Shores. | GIFs | of | pages. |
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http://www.math.unl.edu/~tshores1/linalgtext.html
Linear Algebra and Applications 2008 November
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Textbook by Thomas Shores. GIFs of pages.
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