Practical Linear Algebra: A Geometry Toolbox (Hardcover)

by Gerald Farin (Author), Dianne Hansford (Author)

Editorial Reviews

Product Description
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 online guide is available.

About the Author
Gerald Farin received his Ph.D. in mathematics from the University of Braunschweig, Germany, in 1979. He is the author of Curves and Surfaces for CAGD (5th ed.), NURBS (2nd ed.), The Geometry Toolbox, and The Essentials of CAGD. He is also editor-in-chief of the journal Computer Aided Geometric Design.

Dianne Hansford is a Fulbright scholar who received her Ph.D. in Computer Science from Arizona State University in 1991. She has published several research publications in the field of CAGD and periodically teaches for ASU's computer science department.

Product Details

• Hardcover: 384 pages
• Publisher: AK Peters (December 15, 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: 4.8 out of 5 stars See all reviews (4 customer reviews)
• Amazon.com Sales Rank: #289,847 in Books (See Bestsellers in Books)

  Popular in these categories: (What's this?)

  #81 in	Books > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Algebra > Linear
  #83 in	Books > Science > Mathematics > Pure Mathematics > Algebra > Linear

Customer Reviews

Most Helpful Customer Reviews

5 of 5 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 (REAL NAME)

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.

2 of 2 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 (REAL NAME)

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.

1 of 1 people found the following review helpful:

4.0 out of 5 stars Graphic depictions on almost every single page, March 29, 2008

By	Trip Like I Do (USA) - See all my reviews

Just to add to the existing positive review that the authors of this really good book have chosen to append a visual route and provide relevant diagrams, many of the diagrams amusingly hand-drawn, on nearly every page. Gives the reader a spatial perspective on operations which algebraic purists would look down upon, perhaps because such a presentation reveals how straightforward the subject material actually becomes when tied to concrete graphic representations in three dimensions. Elucidation? Can't have that, now can we?