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Numerical Analysis Hardcover – August 9, 2010

ISBN-13: 978-0538733519 ISBN-10: 0538733519 Edition: 9th

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Editorial Reviews

Review

1. MATHEMATICAL PRELIMINARIES AND ERROR ANALYSIS. Review of Calculus. Round-off Errors and Computer Arithmetic. Algorithms and Convergence. Numerical Software. 2. SOLUTIONS OF EQUATIONS IN ONE VARIABLE. The Bisection Method. Fixed-Point Iteration. Newton's Method and its Extensions. Error Analysis for Iterative Methods. Accelerating Convergence. Zeros of Polynomials and Muller's Method. Survey of Methods and Software. 3. INTERPOLATION AND POLYNOMIAL APPROXIMATION. Interpolation and the LaGrange Polynomial. Data Approximation and Neville's Method Divided Differences. Hermite Interpolation. Cubic Spline Interpolation. Parametric Curves. Survey of Methods and Software. 4. NUMERICAL DIFFERENTIATION AND INTEGRATION. Numerical Differentiation. Richardson's Extrapolation. Elements of Numerical Integration. Composite Numerical Integration. Romberg Integration. Adaptive Quadrature Methods. Gaussian Quadrature. Multiple Integrals. Improper Integrals. Survey of Methods and Software. 5. INITIAL-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS. The Elementary Theory of Initial-Value Problems. Euler's Method. Higher-Order Taylor Methods. Runge-Kutta Methods. Error Control and the Runge-Kutta-Fehlberg Method. Multistep Methods. Variable Step-Size Multistep Methods. Extrapolation Methods. Higher-Order Equations and Systems of Differential Equations. Stability. Stiff Differential Equations. Survey of Methods and Software. 6. DIRECT METHODS FOR SOLVING LINEAR SYSTEMS. Linear Systems of Equations. Pivoting Strategies. Linear Algebra and Matrix Inversion. The Determinant of a Matrix. Matrix Factorization. Special Types of Matrices. Survey of Methods and Software. 7. ITERATIVE TECHNIQUES IN MATRIX ALGEBRA. Norms of Vectors and Matrices. Eigenvalues and Eigenvectors. The Jacobi and Gauss-Siedel Iterative Techniques. Iterative Techniques for Solving Linear Systems. Relaxation Techniques for Solving Linear Systems. Error Bounds and Iterative Refinement. The Conjugate Gradient Method. Survey of Methods and Software. 8. APPROXIMATION THEORY. Discrete Least Squares Approximation. Orthogonal Polynomials and Least Squares Approximation. Chebyshev Polynomials and Economization of Power Series. Rational Function Approximation. Trigonometric Polynomial Approximation. Fast Fourier Transforms. Survey of Methods and Software. 9. APPROXIMATING EIGENVALUES. Linear Algebra and Eigenvalues. Orthogonal Matrices and Similarity Transformations. The Power Method. Householder's Method.The QR Algorithm.Singular Value Decomposition. Survey of Methods and Software. 10. NUMERICAL SOLUTIONS OF NONLINEAR SYSTEMS OF EQUATIONS. Fixed Points for Functions of Several Variables. Newton's Method. Quasi-Newton Methods. Steepest Descent Techniques. Homotopy and Continuation Methods. Survey of Methods and Software. 11. BOUNDARY-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS. The Linear Shooting Method. The Shooting Method for Nonlinear Problems. Finite-Difference Methods for Linear Problems. Finite-Difference Methods for Nonlinear Problems. The Rayleigh-Ritz Method. Survey of Methods and Software. 12. NUMERICAL SOLUTIONS TO PARTIAL DIFFERENTIAL EQUATIONS. Elliptic Partial-Differential Equations. Parabolic Partial-Differential Equations. Hyperbolic Partial-Differential Equations. An Introduction to the Finite-Element Method. Survey of Methods and Software.

About the Author

Richard L. Burden is Emeritus Professor of Mathematics at Youngstown State University. His master's degree in mathematics and doctoral degree in mathematics, with a specialization in numerical analysis, were both awarded by Case Western Reserve University. He also earned a masters degree in computer science from the University of Pittsburgh. His mathematical interests include numerical analysis, numerical linear algebra, and mathematical statistics. Dr. Burden has been named a distinguished professor for teaching and service three times at Youngstown State University. He was also named a distinguished chair as the chair of the Department of Mathematical and Computer Sciences. He wrote the Actuarial Examinations in Numerical Analysis from 1990 until 1999.

J. Douglas Faires, late of Youngstown State University, pursued mathematical interests in analysis, numerical analysis, mathematics history, and problem solving. Dr. Faires won numerous awards, including the Outstanding College-University Teacher of Mathematics by the Ohio Section of MAA and five Distinguished Faculty awards from Youngstown State University, which also awarded him an Honorary Doctor of Science award in 2006.
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Product Details

  • Hardcover: 888 pages
  • Publisher: Cengage Learning; 9 edition (August 9, 2010)
  • Language: English
  • ISBN-10: 0538733519
  • ISBN-13: 978-0538733519
  • Product Dimensions: 10.2 x 8 x 1.5 inches
  • Shipping Weight: 3.5 pounds (View shipping rates and policies)
  • Average Customer Review: 2.8 out of 5 stars  See all reviews (21 customer reviews)
  • Amazon Best Sellers Rank: #57,435 in Books (See Top 100 in Books)

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Customer Reviews

Worst math book I've ever encountered.
Griffin Michl
Many steps are skipped to get to the final answer, but generally the final answer is correct... But at the end of the book, a TON of problems are incorrect.
Christine
The little bit I have been able to go through due to my class load has been well written and understandable.
Mal

Most Helpful Customer Reviews

5 of 5 people found the following review helpful By lee on April 20, 2011
Format: Hardcover Verified Purchase
I'm a grad student and I recently had to learn how to numerically solve PDE's. I'm rather new to computer programming and numerical analysis in general. I've really only been in my field for about 1 year now.

I picked up this book and went straight to Chapter 12. It explained everything quite concisely and had very clear descriptions and diagrams. Armed with pen and paper, I learned how to numerically solve these PDE's quite quickly. It was honestly a fun experience. Whenever there were tools that I was missing, the authors would reference the section and chapter where you could find the necessary tools.

I believe this book was written as a reference, as well as, textbook. A problem that many textbooks suffer from, is that the material is written in sequential order, with newer material depending heavily on the previous chapters. These types of books are not adept to being just picked up and read, to gather the relevant information. They require you to pretty much read all the preceding text to understand it, and who has time for that? This book is NOT like that.

You can just pick it up and easily learn from it. Unlike Numerical Recipes, this provides the method with a very clear explanation and justification for the algorithms. Numerical Recipes is good, but its purpose is not to provide detailed explanations of why and how the algorithms work.

To be able to use this text, I would suggest having taken Calc 1,2 & 3, differential equations, linear algebra class, and be comfortable with programming. I suspect that the folks complaining heavily about this text, are not very comfortable with with Calculus, linear algebra, and/or programming.
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2 of 2 people found the following review helpful By Stefan on February 4, 2011
Format: Paperback Verified Purchase
This paperback book is extremely helpful for getting through this course. It explains things very well and is a great reference for when you get stuck. My only problem is that only part of the questions are worked out. It's not all odds, for example: 1,2,4,5,9,14,16,24,28 are the questions answered for 1.1. It seems that they are the best questions, the ones most likely to be selected by the professor. Every now and then I'll come across a difficult question that got skipped over by this book and it becomes a little aggravating.

Overall, this book is a giant help and is completely worth the $50 that I paid.
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4 of 5 people found the following review helpful By qotd_host on December 15, 2013
Format: Hardcover Verified Purchase
This book has A LOT of mistakes on the author's part--wrong answers...typos...and, the majority of the sections are very confusing with the derivation of the formulas. The worst math textbook I have ever seen in my education career as a student.
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1 of 1 people found the following review helpful By big reader on February 21, 2011
Format: Hardcover
This is a good book, and it is unjust to criticize it too strongly. There is a good set of derivations for the theorems, the explanations of the pseudo-code for the algorithms are helpful, and though the exercises may be computational, they are both exhausting and fun.

Perhaps a weakness is that there is little theoretical emphasis, or discussion within the text of the relations of numerical analysis to other branches of math, nor of detailed proofs. It describes the development of numerical analysis by itself, but does not show it analytical roots as well as it could.

It is a solid book that will help the diligent reader to understand the material.
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6 of 9 people found the following review helpful By Christine on September 30, 2011
Format: Hardcover Verified Purchase
This book was surprisingly annoying...

I'm a CSULB Applied Math, MS student and I expected it to be a lot smoother. The book is written in a very vague fashion, although most of it makes sense...

The point I wanted to review about were the damn solutions, for the most part. I believe the solutions manual seems to be okay so far, but it is also very vague. Many steps are skipped to get to the final answer, but generally the final answer is correct...

But at the end of the book, a TON of problems are incorrect. Chapter 3 is a great show of this. For 3.3, there's an error where one sign is wrong in the polynomial AND a tenths place decimal is missing AND they still get the right answer WITH the wrong sign...On the next problem, which was based on that answer, the correct format is given...

And some things are made much more difficult than need-be...for example, for Lagrange polynomials...why not keep it simple instead of finding an exact answer? The answer isn't really different, in this case. It's easier to check without finding the whole coefficient first.

Many people in my class, including myself initially, were getting caught up trying to "find the right solution." Once we had a conference, we just started checking the answers with each other instead.

Overall, I wasn't very happy with the book. If needed for class, sure. If someone deciding to have it as a school book, no. If checking answers is your thing, don't. And finally, for personal use. Definitely NOT.

Hope this helps.
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2 of 3 people found the following review helpful By Bo on October 30, 2010
Format: Hardcover Verified Purchase
I am using this book for a grad numerical methods class for a masters program in mechanical engineering. The book does not explain very well some of the steps taken during some of examples shown. But it goes into some heavy duty math proofs and concepts. Yeah I like advanced math like the next guy but I think they should spend more time and paper space on algorithms and code definitions as their algorithms are spotty. And some of the Matlab code that is provided on their website does not work. This is a Numerical Analysis book and if they provide programming code then it should work. I spent too much time trying to debug their code that I gave up and started writing my own. So my advice to other people is to study the algorithms shown in the book, come up with a cleaner/better algorithm and write your own code. Do that and then the book will get you through.
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