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Practical scientific computing

A Muhammad, Yanbu University College, Saudi Arabia and V Zalizniak, Siberian Federal University, Russia

 - an invaluable reference for undergraduate engineering, science and mathematics students taking numerical methods courses
 - guides the reader through developing a deep understanding of classical numerical methods
 - features a comprehensive analysis of numEclipse including numerical algorithms and their implementations

Scientific computing is about developing mathematical models, numerical methods and computer implementations to study and solve real problems in science, engineering, business and even social sciences. Mathematical modelling requires deep understanding of classical numerical methods. This essential guide provides the reader with sufficient foundations in these areas to venture into more advanced texts.

The first section of the book presents numEclipse, an open source tool for numerical computing based on the notion of MATLAB®. numEclipse is implemented as a plug-in for Eclipse, a leading integrated development environment for Java programming. The second section studies the classical methods of numerical analysis. Numerical algorithms and their implementations are presented using numEclipse.

Practical scientific computing is an invaluable reference for undergraduate engineering, science and mathematics students taking numerical methods courses. It will also be a useful handbook for postgraduate researchers and professionals whose work involves scientific computing.

ISBN 0 85709 225 1
ISBN-13: 978 0 85709 225 0
February 2011
208 pages  234 x 156mm  paperback  
£55.00 / US$95.00 / €65.00

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An e-book version of this title is available to purchase as part of a Collection or Pick n Mix or by Chapter. Visit Woodhead Publishing Online

About the authors

Dr Ali Muhammad currently works at Yanbu University College, Saudi Arabia. He has previously held leading software development roles in the financial, telecommunication and aviation industries.

Dr Victor Zalizniak is an employee of the Siberian Federal University, Russia. He is the author of several books on scientific computing, including Essentials of Scientific Computing.

Titles which may also be of interest:
Essentials of scientific computing
Computational functional analysis
Circuit analysis
Machine learning and data mining

Contents

PART 1
PART 2

PART 1

Introduction
 - Getting started
 - Interpreter
 - Program

Expressions
 - Matrix
 - Real number
 - Complex number
 - Boolean
 - String
 - Structure
 - Cell
 - Range expression
 - Boolean expression
 - Relational expression
 - Numerical expression

Statements
 - Assignment statement
 - Loop statements
 - Conditional statements
 - Continue and break statements

Programming
 - Program
 - Function
 - Procedure
 - Java programming
 - C Programming

Architecture
 - Front-end
 - Back-end
 - User interface
 - Gnuplot interface
 - Execution engine

Plotting
 - Simple function plot (fplot)
 - 2-Dimensional plots
 - 3-Dimensional plots *

PART 2

Solving nonlinear equations
 - Calculation of roots with the use of iterative functions
 - Exercises

Solving systems of linear equations
 - Linear algebra background
 - Systems of linear equations
 - Error sources
 - Condistion number
 - Iterative methods
 - Exercises

Computational eigenvalue problems
 - Basic facts concerning eigenvalue problems
 - Localizing of eigenvalues
 - Power method
 - Inverse iteration
 - Iteration with a shirt of origin
 - The QR method
 - Exercises

Introduction to finite difference schemes for ordinary differential equations
 - Elementary example of a finite difference scheme
 - Approximation and stability
 - Numerical solution of initial value problems
 - Numerical solution of boundary vlaue problems
 - Error estimation and control
 - Exercises

Interpolation and approximation
 - Interpolation
 - Approximation of funtions and data representation
 - Exercises

Bibliography