Numerical Analysis [Hardcover]

Timothy Sauer (Author)

Book Description

Publication Date: December 17, 2005 | ISBN-10: 0321268989 | ISBN-13: 978-0321268983

Numerical Analysis, designed to be used in a one-year course in engineering, science and mathematics, helps the readers gain a deeper understanding of numerical analysis by highlighting the five major ideas of the discipline: Convergence, Complexity, Conditioning, Compression, and Orthogonality and connecting back to them throughout the text. Each chapter contains a Reality Check, an extended foray into a relevant application area that can be used as a springboard for individual or team projects. MATLAB is used throughout to demonstrate and implement numerical methods.

 

Fundamentals. Solving Equations. Systems of Equations. Interpolation. Least Square. Numerical Differentiation and Integration. Ordinary Differential Equations. Boundary Value Problems. Partial Differential Equations. Random Numbers and Applications. Trigonometric Interpolation and the FFT. Compression. Eigenvalues and Singular Values. Optimization.

 

For all readers interested in numerical analysis.

Editorial Reviews

About the Author

Timothy Sauer earned the Ph.D. degree in mathematics at the University of California, Berkeley in 1982, and is currently a professor at George Mason University. He has published articles on a wide range of topics in applied mathematics, including dynamical systems, computational mathematics, and mathematical biology.

Product Details

• Hardcover: 688 pages
• Publisher: Addison Wesley (December 17, 2005)
• Language: English
• ISBN-10: 0321268989
• ISBN-13: 978-0321268983
• Product Dimensions: 9.3 x 7.6 x 1.5 inches
• Shipping Weight: 2.7 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #446,345 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

10 of 11 people found the following review helpful:

5.0 out of 5 stars An excellent introductory text, November 14, 2006

By 

D. Hundley (Walla Walla, WA United States) - See all my reviews
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This review is from: Numerical Analysis (Hardcover)

I found this book to be very well written- It emphasizes the central themes of Numerical Analysis, and provides insight along with the analysis. I especially liked the projects and "reality checks" that Sauer provides- For example, in the Differential Equations chapter, he provides Matlab code for animating the solutions to the pendulum, double pendulum, and even goes into the "N-body problem". A small critique: The Matlab code could be written better, and some of it needed to be modified to work properly, but these bugs will probably be worked out in future editions. For educators: This book is designed for a year-long course. That being said, I would still highly recommend it for even a one-semester course, even though you will only use half the text.

16 of 21 people found the following review helpful:

5.0 out of 5 stars good introduction to numerical analysis, December 20, 2005

By 

W Boudville (Terra, Sol 3) - See all my reviews
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This review is from: Numerical Analysis (Hardcover)

Sauer teaches numerical analysis with an emphasis on you using Matlab to learn the concepts. His text is suitable as a first course in this subject, at an undergraduate level.

The topics are, by and large, unchanged from those in texts written in the 1970s or even earlier. Like the solving of systems of linear equations. A crucial topic which you should master, because these arise throughout engineering and the physical sciences. So the text goes into the ideas of LU factorisation and Gaussian row reduction with pivoting. Other topics covered included numerical integration and differentiation, and least squares curve fitting.

The rigour of the proofs is also well chosen. Enough to satisfy most students. But without being too abstruse to put most off.

A strong point of the text is the numerous problems interspersed throughout each chapter. These are usefully divided into two types. The first might be considered traditional problems. Where you solve these by hand, with perhaps only a calculator to plug in a few numbers. The second group consists of using Matlab in a more extended foray into numerical analysis. Here, a mere calculator will not suffice. Doing these problems will improve your facility with Matlab and also hopefully garner a general experience in knowing when to use a maths package.

It should also be said that if you already use another package, like Mathematica, then this book can still be germane. Roughly speaking, Mathematica, Matlab and Maple have equivalent functionality. Certainly, this is true at the introductory level of the text.

6 of 7 people found the following review helpful:

5.0 out of 5 stars A very clear textbook, January 9, 2008

By 

Bradley Conte (USA) - See all my reviews
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Amazon Verified Purchase

This review is from: Numerical Analysis (Hardcover)

This textbook is a shining example of what a textbook should be. It is very organized, connects ideas to show the big picture, breaks down topics into the clear, organized elements, provides examples, and is very clearly worded.

My chosen field of study is unrelated to the class I used this book for, but I love it so much I'm going to keep it. If I ever have any questions along these lines in the future, I'll go to it.