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

by Ionut Danaila, Pascal Joly, Sidi Mahmoud Kaber, Marie Postel

Overview

This book demonstrates scientific computing by presenting twelve computational projects in several disciplines including Fluid Mechanics, Thermal Science, Computer Aided Design, Signal Processing and more. Each follows typical steps of scientific computing, from physical and mathematical description, to numerical formulation and programming and critical discussion of results. The text teaches practical methods not usually available in basic textbooks: numerical checking of accuracy, choice of boundary conditions, effective solving of linear systems, comparison to exact solutions and more. The final section of each project contains the solutions to proposed exercises and guides the reader in using the MATLAB scripts available online.

Product Details

ISBN-13:	9780387308890
Publisher:	Springer New York
Publication date:	11/27/2006
Series:	Texts in Applied Mathematics Series , #400
Edition description:	2007
Pages:	294
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

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.

Editorial Reviews

From the reviews:

"In An Introduction to Scientific Computing, the authors present approaches to the numerical solution of problems drawn from a variety of applications. … This is a graduate-level introduction and the pace is brisk. … This is a strong text on scientific computing for advanced students in applied mathematics. … the book is most appropriate for students with some prior experience in scientific computing … ." (William J. Satzer, MathDL, February, 2007)

"The book is based on material offered by the authors at Universite Pierre et Marie Curie (Paris, France) and different engineering schools. It is intended as a graduate-level text in applied mathematics, but it may also be used by students in engineering or physical sciences. It may also be used as a reference for researchers and practicing engineers. Since different possible levels of each project are suggested, the text can be used to propose assignments at different graduate levels." (I. N. Katz, Zentralblatt MATH, Vol. 1119 (21), 2007)

"An Introduction to Scientific Computing plunges into solving PDEs by numerical approximation. … the book is an attempt to completely discuss numerical issues for reasonably complex problems at the level of a graduate textbook. A project-based approach is used. … Overall, this is a pleasing and useful companion to more complete expositions of the topic. … If you’re preparing advanced students for a workshop, or organizing a numerical analysis club for the semester, then the book is perfect." (Sorin Mitran, SIAM Review, Vol. 50 (1), 2008)

From the Publisher