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Numerical Analysis [Paperback]

Richard Burden , J.Douglas Faires
5.0 out of 5 stars  See all reviews (1 customer review)
Price: £60.00 & FREE Delivery in the UK. Details
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Book Description

15 Dec 2010 0538735643 978-0538735643 International ed of 9th revised ed
This well-respected text gives an introduction to the modern approximation techniques and explains how, why, and when the techniques can be expected to work. The authors focus on building students' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. With a wealth of examples and exercises, the text demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. The applications chosen demonstrate concisely how numerical methods can be, and often must be, applied in real-life situations. In this edition, the presentation has been fine-tuned to make the book even more useful to the instructor and more interesting to the reader. Overall, students gain a theoretical understanding of, and a firm basis for future study of, numerical analysis and scientific computing. A more applied text with a different menu of topics is the authors' highly regarded "Numerical Analysis, Third Edition".

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Numerical Analysis + Numerical Solution of Partial Differential Equations: Finite Difference Methods 3rd Edition (Oxford Applied Mathematics and Computing Science Series)
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Product details

  • Paperback: 888 pages
  • Publisher: Brooks/Cole; International ed of 9th revised ed edition (15 Dec 2010)
  • Language: English
  • ISBN-10: 0538735643
  • ISBN-13: 978-0538735643
  • Product Dimensions: 25.2 x 20.2 x 3.6 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Bestsellers Rank: 56,635 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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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.

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5.0 out of 5 stars Excellent 5 May 2011
By pen
Format:Paperback|Verified Purchase
Brand new as stated. Very good service, arrived promply and well within the timescale indicated. Would recommend this supplier to others.
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Amazon.com: 2.8 out of 5 stars  18 reviews
4 of 4 people found the following review helpful
2.0 out of 5 stars Worst book ever! 15 Dec 2013
By qotd_host - Published on Amazon.com
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.
4 of 4 people found the following review helpful
5.0 out of 5 stars Good Refernce book 20 April 2011
By lee - Published on Amazon.com
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. If you are an undergrad and have not taken those classes or are not comfortable with the material, I can see you struggling. If you are a grad student in Math or Physics, this text will be rather refreshingly easy to read. It will help fill in the necessary gaps in your knowledge of computational work, if you have any like I did. Enjoy!
2 of 2 people found the following review helpful
4.0 out of 5 stars Such a help, although incomplete. 4 Feb 2011
By Stefan - Published on Amazon.com
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.
6 of 8 people found the following review helpful
2.0 out of 5 stars Don't get caught up on solutions... 30 Sep 2011
By Christine - Published on Amazon.com
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.
1 of 1 people found the following review helpful
5.0 out of 5 stars This is a great book. Most of the negative reviews are about ... 8 Aug 2014
By jacob - Published on Amazon.com
This is a great book. Most of the negative reviews are about it leaving things out or the solutions are wrong. To that I say, in most upper level math books the authors are going to begin leaving things out. If you truly want to understand the concepts do the proofs or examples yourself. That is what I did using this book and I learned more from the course that used this book than any other course. And if your complaint is that the solutions are wrong I cannot take your review seriously. Don't use solution manuals. You should be confident enough in your abilities to not need to see the answers.

For my Master's thesis I am doing work in optimal control theory and I wanted to go back and write some of my old codes again to make them faster. I read the sections pertaining to ODEs and it covered them well enough to understand the algorithms and I wrote the codes in no time.

To sum it up, this book is great if you are not lazy.
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