Practical Linear Algebra: A Geometry Toolbox [Hardcover]

Gerald Farin (Author), Dianne Hansford (Author)

Book Description

ISBN-10: 1568812345 | ISBN-13: 978-1568812342 | Publication Date: December 21, 2004

Practical Linear Algebra introduces students in math, science, engineering, and computer science to Linear Algebra from an intuitive and geometric viewpoint, creating a level of understanding that goes far beyond mere matrix manipulations. Practical aspects, such as computer graphics topics and numerical strategies, are covered throughout, and thus students can build a "Geometry Toolbox," based on a geometric understanding of the key concepts. This book covers all the standard linear algebra material for a first-year course; the authors teach by motivation, illustration, and example rather than by using a theorem/proof style. Special Features: - Clear visual representations (more than 200 figures) for improved material comprehension. - Hand-drawn sketches encourage students to create their own sketches when solving problems-developing another layer of learning. - Numerous examples show applications to real-world problems. - Problems at the end of each chapter allow students to test their understanding of the material presented. Solutions to selected problems are provided. - Concise chapter summaries highlight the most important points, giving students focus for their approach to learning. An instructor's manual will be available soon.

Editorial Reviews

Review

" Read an article on teaching Linear Algebra written by Gerald Farin and Dianne Hansford. -Ties Magazine, November 2005
""It is well written and the examples are carefully chosen to motivate or exemplify the topic at hand."" -J.R. Burke, CHOICE Magazine , September 2005
""[The] mixture of linear algebra, geometry, and numerical aspects is very interesting and will probably stimulate the students."" -Yves Felix, Bulletin of the Belgian Mathematical Society, December 2005
""I picked up this book with the thought, 'oh, another linear algebra text.' I was pleasantly surprised, upon examination, that it is not just another one. The standard linear algebra material is presented with good motivating stories, illustrations and examples."" -S. Swaminathan, CMS Notes, February 2006
""This book covers all the fundamental topics of linear algebra ... It is also an inspiring book for pure mathematicians who would like to learn more about applications of linear algebra ... a useful source of many nice examples."" -EMS, December 2006
""Das Buch [ist] eine einmalige und wertvolle Ergänzung zur bestehenden reichen Literatur zur Linearen Algebra."" -Internationale Mathematische Nachrichten, April 2007"

About the Author

Gerald Farin received his Pd.D. in Mathematics from the University of Braunschweig, Germany, in 1979. He is the author of the texts "Curves and Surfaces for CAGD" (5th ed.), "NURBS" (2nd ed.), "The Geometry Toolbox", and "Essentials for CAGD". He is the editor-in-chief of "Computer Aided Geometric Design". Dianne Hansford received her Ph.D. in Computer Science from Arizona State University in 1991. Since 1995 she has been a faculty associate at ASU's computer science department, occasionally teaching Computer Aided Geometric Design (CAGD) and Computer Graphics. She has published several research papers in the field of CAGD and is coauthor of the books "The Geometry Toolbox" and "Essentials for CAGD".

Product Details

• Hardcover: 394 pages
• Publisher: A K Peters/CRC Press (December 21, 2004)
• Language: English
• ISBN-10: 1568812345
• ISBN-13: 978-1568812342
• Product Dimensions: 9.6 x 7.4 x 1 inches
• Shipping Weight: 1.9 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #714,756 in Books (See Top 100 in Books)

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Customer Reviews

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9 of 9 people found the following review helpful:

5.0 out of 5 stars Perfect introduction to linear algebra, July 21, 2008

By 

Joshua Davies (Dallas, TX United States) - See all my reviews
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This review is from: Practical Linear Algebra: A Geometry Toolbox (Hardcover)

I have to say this book was perfect. It's written with the assumption that you know algebra and trigonometry (you'll also need a little bit of calculus if you want to completely absorb chapter 18) and goes from there to describe linear algebra step-by-step. I was struggling with concepts like Eigenvectors, Gaussian elimination, matrix inversion, etc. but after reading through this book and working all the exercises (most of which have answers in the back for self-study), I'm actually finding myself "thinking" in linear algebra.

The first third or so of the book covers 2D linear algebra, and has a bit of a bias towards graphics problems. It covers things like line intersections and "closest point to a line" as well as rotations, shears, translations, etc. The next third or so extends these concepts out to 3D (still with sort of a graphics bias) and introduces 3D-only concepts such as the cross product. Finally, the last third introduces the abstract N-dimensional perspective that doesn't have a graphical interpretation. This is where it discusses things like least-squares estimation and orthonormalization - the really useful (but abstract) bits of linear algebra.

With the first two thirds of the book to back it up, I found the really abstract concepts (which most authors seem to want to start with) relatively easy to absorb - which is really a pretty amazing accomplishment.

I also can't recommend the chapter exercises highly enough. Most of them had answers in the back, so you can check your work (including these ought to be a no-brainer for writers of math books, but evidently there are quite a few math book writers with, well, no brains...) There was a perfect mix of "check your understanding" type questions and "stretch your brain a bit" exercises, but the book itself was entirely self-contained; as long as you're comfortable with basic trigonometry, you'll have no trouble figuring out the answers to the authors questions with just the material in the chapter.

9 of 9 people found the following review helpful:

5.0 out of 5 stars Add Linear Algebra to your Tool Box., January 15, 2008

By 

J. Wrenholt (Lincoln, NE United States) - See all my reviews
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This review is from: Practical Linear Algebra: A Geometry Toolbox (Hardcover)

This is a very good book for learning Linear Algebra. It succeeds is two important ways. One it helps you build an intuitive understanding of the subject, something more theoretical books sometimes fail to do. Second, it helps you build a nice toolkit for working with 2D and 3D geometric models.

So, it covers the normal topics of Linear Algebra, vectors, matrices, determinants, Gaussian elimination, eigenvalues, etc. But, it also mixes in topics from Computer Graphics such as points, lines, planes, polygons and Bezier curves. By doing so, it demonstrates just how useful Linear Algebra is for geometric transformations such as scaling, rotation, and translation.

Math majors will want to go beyond this book. There are several books that give a more comprehensive treatment of this subject. But, even to those readers, I suggest you try this one first.

1 of 1 people found the following review helpful:

5.0 out of 5 stars Applications of linear algebra you can see, June 2, 2011

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
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This review is from: Practical Linear Algebra: A Geometry Toolbox (Hardcover)

Linear algebra has traditionally been the class in the undergraduate math curriculum where the student makes the transition from "plug - n - chug" formula popping to mathematical proofs. However, in recent years linear algebra has taken on a new role, namely as the best class where applied mathematics can be visually demonstrated. The enormous advances in animated imagery have led to movies where the characters are a virtual hybrid of animated and real. I once taught a course in computer graphics for computer programmers and they were impressed when they applied a basic matrix multiplication to a figure and could watch the altered figure appear on the screen, albeit slowly. Quite frankly, they loved the course.
This book covers linear algebra before the appearance of formal proofs; I cannot recall seeing a single proof. That coverage is excellent and is focused on how images are created and modified using linear algebra. It is clearly written and illustrated and a tutorial on PostScript appears in an appendix. There is a set of exercises at the end of each chapter and solutions to many of them are included.
A textbook for the modern use of linear algebra as an image creation and modification tool, it is ideal for any math program that wants to cover that material. In my experience, it would be a very popular course, but it cannot be used for any coverage of linear algebra that involves proofs.

Published in Journal of Recreational Mathematics, reprinted with permission