An Introduction to Scientific Computing: Twelve Computational Projects Solved with MATLAB

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Springer Science & Business Media, Dec 3, 2007 - Mathematics - 294 pages
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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 image processing, 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.
 

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Contents

Numerical Approximation of Model Partial Differential
1
Application to Chemical
33
Polynomial Approximation
49
4
84
Solving a Differential Equation by a Spectral Method
111
Multiresolution Analysis 127
126
Elastic Deformation of a Thin Plate
151
Domain Decomposition Using a Schwarz Method
165
Bézier Curves and Surfaces
193
The Riemann Problem and Discontinuous
213
Chapter References
233
Chapter References
250
12
251
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