This book demonstrates scientific computing by presenting twelve computational projects spanning a broad spectrum of disciplines including Fluid Mechanics, Chemistry, Elasticity, Thermal Science, Computer Aided Design, Signal and Image Processing, and offers practical methods not usually included in basic textbooks.

Teaching or learning numerical methods in applied mathematics cannot be conceived nowadays without numerical experimentation on computers. There is a vast literature devoted either to theoretical numerical methods or - merical programming of basic algorithms, but there are few texts o?ering a complete discussion of numerical issues involved in the solution of concrete and relatively complex problems. This book is an attempt to ?ll this need. It is our belief that advantages and drawbacks of a numerical method cannot be accounted for without one's experiencing all the steps of scienti?c comp- ing, from physical and mathematical description of the problem to numerical formulation and programming and, ?nally, to critical discussion of numerical results. The book provides twelve computational projects aimed at numerically solving problems selected to cover a broad spectrum of applications, from ?uid mechanics, chemistry, elasticity, thermal science, computer-aided design, signal and imageprocessing, etc. Even though the main volume of this text concerns the numerical analysis of computational methods and their imp- mentation, we have tried to start, when possible, from realistic problems of practical interest for researchers and engineers. For each project, an introductory record card summarizes the mathem- ical and numerical topics explained and the ?elds of application of the - proach. A level of di?culty, scaling from 1 to 3, is assigned to each project.

MATLAB computer programs for each application-project are made available from the Web site of the Editor Versions using the share-ware language Scilab are provided Complementary bibliography is provided with each project Web page for the book: http://www.ann.jussieu.fr/AI2SC provides an introduction to the book, a chapter content and for each chapter compressed archives containing the MATLAB solutions Chapter summaries, detailed illustrations, and study guides at the end of sections included Exericeses and selected solutions provided Includes supplementary material: sn.pub/extras

Klappentext

This book provides twelve computational projects aimed at numerically solving problems from a broad range of applications including Fluid Mechanics, Chemistry, Elasticity, Thermal Science, Computer Aided Design, Signal and Image Processing. For each project the reader is guided through the typical steps of scientific computing from physical and mathematical description of the problem, to numerical formulation and programming and finally to critical discussion of numerical results. Considerable emphasis is placed on practical issues of computational methods. The last section of each project contains the solutions to all proposed exercises and guides the reader in using the MATLAB scripts. The mathematical framework provides a basic foundation in the subject of numerical analysis of partial differential equations and main discretization techniques, such as finite differences, finite elements, spectral methods and wavelets).

The book is primarily intended as a graduate-level text in applied mathematics, but it may also be used by students in engineering or physical sciences. It will also be a useful reference for researchers and practicing engineers.

Inhalt
Numerical Approximation of Model Partial Differential Equations.- Nonlinear Differential Equations: Application to Chemical Kinetics.- Polynomial Approximation.- Solving an Advection-Diffusion Equation by a Finite Element Method.- Solving a Differential Equation by a Spectral Method.- Signal Processing: Multiresolution Analysis.- Elasticity: Elastic Deformation of a Thin Plate.- Domain Decomposition Using a Schwarz Method.- Geometrical Design: Bézier Curves and Surfaces.- Gas Dynamics: The Riemann Problem and Discontinuous Solutions: Application to the Shock Tube Problem.- Thermal Engineering: Optimization of an Industrial Furnace.- Fluid Dynamics: Solving the Two-Dimensional Navier-Stokes Equations.