Mathematics

For in-depth Linear Algebra courses that focus on applications.

This text aims to teach basic methods and algorithms used in modern, real problems that are likely to be encountered by engineering and science students—and to foster understanding of why mathematical techniques work and how they can be derived from first principles. No text goes as far (and wide) in applications. The authors present applications hand in hand with theory, leading students through the reasoning that leads to the important results, and provide theorems and proofs where needed. Because no previous exposure to linear algebra is assumed, the text can be used for a motivated entry-level class as well as advanced undergraduate and beginning graduate engineering/applied math students.

• Abundant exercises—Appear after almost every subsection, in a wide range of difficulty.

  • Starts each exercise set with straightforward computational problems to test and reinforce the new techniques and ideas.

  • Presents more advanced and more theoretical exercises later on in the set.

  • Includes numerous computer-based exercises and in-depth projects.

• Discussion of the basics of matrices, vectors, and Gaussian elimination.

• Coverage of less-familiar topics from linear systems theory—Includes the LU decomposition and its permuted versions.

• Wide range of illustrative examples to explain essential concepts of vector space, subspace, span, linear independence, basis, and dimension—Addresses the difficulty students often have with these concepts.

• Concurrent development of the finite-dimensional and function space cases in Chapters 2 and 3 (Inner Products and Norms).

• An entire chapter (Chapter 6) devoted to applications of the concepts of Minimization and Least Squares and Orthogonality.

• Flexible presentation of Linear Functions, Linear Transformations, and Linear Systems (Chapter 7)—Can be covered or omitted as desired.

• Coverage of eigenvalues and their applications in linear dynamical systems governed by ordinary differential equations and iterative systems, such as Markov chains and numerical solution algorithms.

• Complete discussions of numerical linear algebra, including pivoting strategies, condition numbers, iterative solution methods such as Gauss- Seidel and SOR, singular value decomposition, the QR algorithm, and finite elements.

• Unique chapter on Boundary Value Problems in One Dimension (Chapter 11). Presents topics from applied linear analysis such as delta functions, Green's function, and finite elements, as a completely natural development of linear algebra in function spaces.

• Text-specific website at http://www.math.umn.edu/~olver/ala.html—Contains a number of illustrative MATLAB problems the authors used in teaching the course.

Chapter 1. Linear Algebraic Systems

Chapter 2. Vector Spaces and Bases

Chapter 3. Inner Products and Norms

Chapter 4. Minimization and Least Squares Approximation

Chapter 5. Orthogonality

Chapter 6. Equilibrium

Chapter 7. Linearity

Chapter 8. Eigenvalues

Chapter 9. Linear Dynamical Systems

Chapter 10. Iteration of Linear Systems

Chapter 11. Boundary Value Problems in One Dimension

Introductory Linear Algebra  (Mathematics)

Some Quotes from Reviewers

“The material on the concept of a general vector space, linear independence, basis, etc. is always difficult for students in this course. This book handles it very well. It gives full, clear explanations. The style is very good, clear, and thorough. It should appeal to my students. I like the book very much. It subscribes to the same philosophy of linear algebra as pioneered by Strang some 30 years ago (acknowledged in the introduction) and builds on the Strang books, making things even clearer and adding more topics. I would certainly like to use this book and would recommend it to my colleagues.”

            -Bruno Harris, Brown University

 

“I like the book very much. We will consider it for our linear algebra courses. This is the best new book to appear since the text by Gilbert Strang. It is really modern book, combining, in a masterful, core and applied aspects of linear algebra. This is a very good book written by a very good mathematician and a very good teacher.”

-Juan J. Manfredi, University of Pittsburgh

 

“In many, if not most, beginning texts of linear algebra, the applications may be collected together in a chapter at the end of the book or in an appendix, leaving any inclusion of this material to the discretion of the instructor. However, Applied Linear Algebra by Olver and Shakiban completely reverses this procedure with a total integration of the application with the abstract theory. The effect on the reader is quite amazing. The reader slowly begins to realize two main points: (1) how applications generally drive the abstract theory, and (2) how the abstract theory can illuminate the applications, and resolve solutions in very striking ways.

 

This text is easily the best beginning linear algebra text dealing with the applications in an integrated way that I have seen. There is no doubt that this text will be the standard to which all beginning linear algebra texts will be compared. Simply put, this is an absolutely wonderful text!”

-Norman Johnson, University of Iowa

 

“I lover the style of this book, especially the fact that you could feel the authors’ enthusiasm about the nice mathematics involved in the theory. The examples were very clear and interesting, and they always tried to approach the same problems over and over again as soon sas they had more weapons at their disposal to attack them. I thought this was great, this text introduces the notion of an abstract space very early (still, after Gaussian Elimination) and in a very natural way, then emphasizes along the way over and over again that tremendously. I would absolutely consider this text. I was really taken by the applications and the organization of the materials. I also loved the abundance of exercises and problems.”

-Tamas Wiandt, Rochester Institute of Technology

 

“This text is very well-written, has lots of examples, and is easy to read and learn from. I’d use it in my Matrix Methods class. There is a good mixture of routine and more advanced examples.”

-James Curry, University of Colorado-Boulder

 

“I believe the writing style would appeal to my students because of the clarity and the examples, as well as the tone. I am going to consider its use, once I see its final form.”

-Fabio Augusto Miner, Purdue University

Instructor's Solutions Manual
Olver & Shakiban
©2005 | Prentice Hall | Paper; 388 pp | Instock
ISBN-10: 013148432X | ISBN-13: 9780131484320
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Instructors Solution Manual, Catalog download
Olver
©2005 | Prentice Hall | On-line Supplement | Instock
ISBN-10: 0131473832 | ISBN-13: 9780131473836
URL:  http://www.prenhall.com/olver

Student Solutions Manual
Olver & Shakiban
©2005 | Prentice Hall | Paper; 178 pp | Instock
ISBN-10: 0131473840 | ISBN-13: 9780131473843
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Addison-Wesley's Algebra Review
Addison-Wesley
©2004 | Prentice Hall | Paper | Out of Stock
ISBN-10: 0321247086 | ISBN-13: 9780321247087

Addison-Wesley's Basic Math Review
Addison-Wesley
©2004 | Prentice Hall | Paper | Instock
ISBN-10: 0321247078 | ISBN-13: 9780321247070

Algebra Review Study Card, 2/E
D'Ippolito & Generazzo
©2006 | Prentice Hall | Study Card; 6 pp | Instock
ISBN-10: 0321394739 | ISBN-13: 9780321394736
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Allied Health Study Card, 2/E
Forshier
©2006 | Prentice Hall | Study Card | Instock
ISBN-10: 0321394747 | ISBN-13: 9780321394743
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Basic Math Review Card, 2/E
Addison-Wesley
©2006 | Prentice Hall | Study Card; 6 pp | Instock
ISBN-10: 0321394763 | ISBN-13: 9780321394767
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Concept Videos: Algebra
Addison-Wesley
©2008 | Prentice Hall | Multiple Media Package | Instock
ISBN-10: 0321517199 | ISBN-13: 9780321517197

Concept Videos: Basic Math & Prealgebra
Addison-Wesley
©2008 | Prentice Hall | Multiple Media Package | Instock
ISBN-10: 032151758X | ISBN-13: 9780321517586

Discovering Algebra: Examples with Keystrokes on the TI-83/TI-82 and TI-85/TI-86, A Laboratory Approach
Pirich & Bigliani
©1997 | Prentice Hall | Paper; 195 pp | Instock
ISBN-10: 0136492037 | ISBN-13: 9780136492030
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Finite Mathematics Study Card
Addison-Wesley
©2006 | Prentice Hall | Study Card | Instock
ISBN-10: 0321374398 | ISBN-13: 9780321374394
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Flash Review Series: Algebra
Becker
©2004 | Prentice Hall | Paper | Instock
ISBN-10: 0321143094 | ISBN-13: 9780321143099
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Graphing Calculator Reference Card, 3/E
Ripley
©2006 | Prentice Hall | Study Card; 6 pp | Instock
ISBN-10: 0321394755 | ISBN-13: 9780321394750
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Graphing Calculator Tutorial CD
Addison-Wesley
©2006 | Prentice Hall | CD-ROM Only | Instock
ISBN-10: 0321357744 | ISBN-13: 9780321357748
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Interwrite Personal Response System
EduCue, Addison-Wesley & Benjamin Cummings
©2004 | Prentice Hall | Electronic Supplement | Instock
ISBN-10: 0321267354 | ISBN-13: 9780321267351

Math for Allied Health Study/Reference Card
Forshier
©2006 | Prentice Hall | Study Card; 0 pp | Out of Stock
ISBN-10: 0321336542 | ISBN-13: 9780321336545

Mathematics Spanish Glossary, 2/E
Lara & Peeples
©2000 | Prentice Hall | Paper; 48 pp | Instock
ISBN-10: 0201728966 | ISBN-13: 9780201728965
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Overcoming Math Anxiety, 2/E
Davidson & Levitov
©2000 | Prentice Hall | Paper | Instock
ISBN-10: 0321069188 | ISBN-13: 9780321069184
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Pearson TI Rebate Coupon $15, 2/E
Pearson
©2009 | Prentice Hall | Paper | Instock
ISBN-10: 0321566041 | ISBN-13: 9780321566041

Prealgebra Review Workbook
Wheel
©2006 | Prentice Hall | Paper; 300 pp | Instock
ISBN-10: 0321473329 | ISBN-13: 9780321473325
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Review of Algebra, A
Howard
©2002 | Prentice Hall | Paper; 224 pp | Instock
ISBN-10: 0201773473 | ISBN-13: 9780201773477
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Saleable Technology Bundle, 2/E
Pearson
©2009 | Prentice Hall | Multiple Media Package | Estimated Availability : 09/01/2008
ISBN-10: 0321561880 | ISBN-13: 9780321561886

Spanish Basic Math Study Card
Leonarte
©2007 | Prentice Hall | Study Card | Instock
ISBN-10: 0321438582 | ISBN-13: 9780321438584
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Stand-alone Access Code Tutor Center
Addison-Wesley
©2008 | Prentice Hall | Access Code Card | Instock
ISBN-10: 0201721708 | ISBN-13: 9780201721706
URL:  http://www.aw-bc.com/tutorcenter
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For Introductory Linear Algebra

Understanding Linear Algebra Using MATLAB
Kleinfeld & Kleinfeld
©2001 | Prentice Hall | Paper; 210 pp | Instock
ISBN-10: 0130609455 | ISBN-13: 9780130609458

Visualizing Linear Algebra Using Maple
Keith
©2001 | Prentice Hall | Paper; 250 pp | Out of Stock
ISBN-10: 0130418161 | ISBN-13: 9780130418166

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