Mathematical Principles for Scientific Computing and Visualization - Gerald E. Farin

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Résumé :
This non-traditional introduction to the mathematics of scientific computation describes the principles behind the major methods, from statistics, applied mathematics, scientific visualization, and elsewhere, in a way that is accessible to a large part of the scientific community. Introductory material includes computational basics, a review of coordinate systems, an introduction to facets (planes and triangle meshes) and an introduction to computer graphics. The scientific computing part of the book covers topics in numerical linear algebra (basics, solving linear system, eigen-problems, SVD, and PCA) and numerical calculus (basics, data fitting, dynamic processes, root finding, and multivariate functions). The visualization component of the book is separated into three parts: empirical data, scalar values over 2D data, and volumes.

There are several software packages in wide use that make scientific computation and visualization easier to perform. However, the premise of Farin and Hansford is that without a basic understanding of the mathematics of a problem, the use of these packages could very well give unrecognized erroneous results. ... There are numerous examples, and the exercises are designed to stimulate insight into the issues, rather than provide drill and practice. Mathematical Principles for Scientific Computing and Visualization is unique in its approach and written in an informal style ... Highly recommended. -CHOICE, June 2009 ... a non-traditional introduction to the math of scientific computation and comes packed with many examples to provide readers with the right tools for using the software packages behind the computations. College-level collections strong in software engineering, science, math or computers will find it an excellent technical pick. -California Bookwatch, February 2009