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This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of differential equations. To make the presentation concrete and appealing, the programming environment Matlab is adopted as a faithful companion. All the algorithms introduced throughout the book are shown, thus furnishing an immediate quantitative assessment of their theoretical properties such as stability, accuracy and complexity. The book also contains the solution to several problems raised through exercises and examples, often originating from specific applications. A specific section is devoted to subjects which were not addressed in the book and indicate the bibliographical references for a more comprehensive treatment of the material.
Date: 2005-04-10 Rating: 4
Review: easy to understand and use algorithms
As you would expect from Springer, here is a technically very accurate book. It goes over the main concepts of numerical analysis, which the authors call “scientific computing”. Same thing, really. Unlike earlier years, where someone studying this field would have to write out her own Fortran code to apply the methods, we now have MATLAB. The authors chose this powerful package as one in which to explain and implement the algorithms.
These algorithms are essentially unchanged from what a book on the topic might have described, 20 years ago. Finding numerical integrals, roots of equations, solving linear systems of equations etc.
But using MATLAB helps streamline any coding. And you are encouraged to code, in the problems supplied by the book. There are even answers to some of these. So quite apart from understanding the concepts, a bonus is that you can become quite adept at fully using MATLAB’s abilities as a research tool.