Numerical Analysis 
asked by teacher on November 22, 2006 12:39 AM
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 METHODS, Third Edition.
Reviews
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I examined this book as part of my constant quest for better textbooks. In this case, the course is a one-semester course in numerical analysis. I have been using "Elementary Numerical Analysis Third Edition" by Atkinson and Han and am generally pleased with the results. The first point to make is that this book has more material than I could ever cover in one semester, so from my perspective it is unsuitable. However, if you have a two semester sequence in numerical analysis, then it has enough material so that it could be used both semesters.
There are twelve chapters:
*) Mathematical preliminaries
*) Solutions of equations in one variable
*) Interpolation and polynomial approximation
*) Numerical differentiation and integration
*) Initial-value problems for ordinary differential equations
*) Direct methods for solving linear systems
*) Iterative techniques in matrix algebra
*) Approximation theory
*) Approximating eigenvalues
*) Numerical solutions of nonlinear systems
*) Boundary-value problems for ordinary differential equations
*) Numerical solutions to partial differential equations
with an exercise set at the end of each section and the solutions to the odd numbered problems included at the end.
The level is more rigorous than Atkinson and Han, more of the results are first expressed in the form of theorems as opposed to the Atkinson approach of using worked examples. Once the theorem is presented, Burden then goes on to demonstrate by example. Burden uses Maple code to present the algorithms, which is generally understandable. Since the code is presented in snippets used to solve a specific problem, a lack of experience in Maple is not a serious hindrance. It is easy to infer the meaning of the Maple commands from the context.
However, it lacks the easy readability of the Atkinson book. There were many occasions when I stopped and had to think about what I had read. It eventually made sense, but I had to think about it before it was clear. I don't have that problem with the Atkinson book. Therefore, even if we made a change to a two semester sequence in numerical analysis, I doubt if I would adopt this book.
There are twelve chapters:
*) Mathematical preliminaries
*) Solutions of equations in one variable
*) Interpolation and polynomial approximation
*) Numerical differentiation and integration
*) Initial-value problems for ordinary differential equations
*) Direct methods for solving linear systems
*) Iterative techniques in matrix algebra
*) Approximation theory
*) Approximating eigenvalues
*) Numerical solutions of nonlinear systems
*) Boundary-value problems for ordinary differential equations
*) Numerical solutions to partial differential equations
with an exercise set at the end of each section and the solutions to the odd numbered problems included at the end.
The level is more rigorous than Atkinson and Han, more of the results are first expressed in the form of theorems as opposed to the Atkinson approach of using worked examples. Once the theorem is presented, Burden then goes on to demonstrate by example. Burden uses Maple code to present the algorithms, which is generally understandable. Since the code is presented in snippets used to solve a specific problem, a lack of experience in Maple is not a serious hindrance. It is easy to infer the meaning of the Maple commands from the context.
However, it lacks the easy readability of the Atkinson book. There were many occasions when I stopped and had to think about what I had read. It eventually made sense, but I had to think about it before it was clear. I don't have that problem with the Atkinson book. Therefore, even if we made a change to a two semester sequence in numerical analysis, I doubt if I would adopt this book.
reviewed by trailrider on November 28, 2006 4:13 PM
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Examples are few and offer little explaination.
I find this book so hard to follow.
On a good note: algorithms are clear.
I find this book so hard to follow.
On a good note: algorithms are clear.
reviewed by success06 on November 29, 2006 3:19 AM
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I dont think the other reviewers are quite accurate in their assessment of this text. The book does offer many examples, and the pseudocode is very helpful in implementing these methods. The real problem with this book is that many of the explanations of the methods are written in pseudocode. This makes learning the concepts extremely confusing and difficult, as they are written in code. The proofs are helpful, but with the confusing notation in iterative methods, there is no way near enough information to correctly learn what is going on. I took this class in graduate school and never used the book unless I wanted to see some code. My advice: Take notes from the professor, and if you need to code up a method, go to the library and copy down what you need. A VERY poor teaching aid!
reviewed by geo on November 29, 2006 5:16 PM