Numerical Mathematics (Texts in Applied Mathematics) | 
 enlarge | Authors: Alfio Quarteroni, Riccardo Sacco, Fausto Saleri
Publisher: Springer
Category: Book
List Price: $89.95
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Rating:  1 reviews
Sales Rank: 855410
Media: Hardcover
Edition: 2nd
Pages: 657
Number Of Items: 1
Shipping Weight (lbs): 2.5
Dimensions (in): 9.3 x 6.5 x 1.6
ISBN: 3540346589
Dewey Decimal Number: 511
EAN: 9783540346586
Publication Date: November 10, 2006
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Product Description
Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions. As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis. One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performances on examples and counterexamples which outline their pros and cons. This is done using the MATLAB software environment which is user-friendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified on a MATLAB computer implementation. Every chapter is supplied with examples, exercises and applications of the discussed theory to the solution of real-life problems. This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in Engineering, Mathematics, Physics and Computer Sciences. The attention which is paid to the applications and the related development of software makes it valuable also for researchers and users of scientific computing in a large variety of professional fields. In this second edition, the readability of pictures, tables and program headings have been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been added.
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| Customer Reviews:
Style of presentation is confusing; reads like a reference, not a learning book October 29, 2006
Alexander C. Zorach (New Haven, CT)
4 out of 8 found this review helpful
This book appears to be very comprehensive, encompassing topics not usually found in the same volume, including numerical linear algebra, nonlinear optimization, numerical integration, and numerical solutions to ODE's and PDE's. The authors claim that this book is intended as a textbook for undergraduates wishing to engage in scientific computing, but the book's style of presentation is more appropriate for an advanced reference than a learning text. At the same time, the book is not thorough enough to be used as a reference.
In many chapters, the authors begin a topic in a general abstract framework, introduce concepts such as stability or convergence, and only later present specific methods and algorithms. The presentation and explanation of certain topics is very clear, but one has to skip around and sort through a lot of confusing nonsense to find the worthwhile parts of this text. Many ideas that could be expressed clearly in words are instead put in equation form where they are cryptic and unintuitive. The algorithms and diagrams are a little more useful and easier to understand, but often the book ignores discussion of the practicality of the various algorithms, and sometimes it ignores simple enhancements that have become common practice, instead only presenting algorithms in forms that are impractical and seldom used.
There is a wealth of other books covering much of the other material in this text. Where the material overlaps with Golub's "Matrix Computations", Golub's book is far superior, starting from a more basic level, covering the material in more depth, exploring more possibilities, and providing a much healthier dose of explicit algorithms. Trefethen's textbook "Numerical Linear Algebra" covers similar material in a much better fashion. The material on numerical optimization is covered in a much more readable fashion in the book by Nocedal and Wright, although that book definitely moves much slower. I can't say about the material on numerical methods for differential equations because it is an area I have not worked with.
This book might make a good reference for people who are already well-versed with many of the methods in this book and who wish to look up one topic here or there. However, I can say that I did not find it a useful text to learn the material from, and I doubt anyone would.
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