Description

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.

Key Features

  • 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

Readership

Professionals and academics.

Table of Contents

Preface

Acknowledgements

Part I

Chapter 1: Introduction

1.1 Getting Started

1.2 Interpreter

1.3 Program

Chapter 2: Expressions

2.1 Matrix

2.2 Real Number

2.3 Complex Number

2.4 Boolean

2.5 String

2.6 Structure

2.7 Cell

2.8 Range Expression

2.9 Boolean Expression

2.10 Relational Expression

2.11 Numerical Expression

Chapter 3: Statements

3.1 Assignment Statement

3.2 Loop Statements

3.3 Conditional Statements

3.4 Continue and Break Statements

Chapter 4: Programming

4.1 Program

4.2 Function

4.3 Procedure

4.4 Java Programming

4.5 C Programming

Chapter 5: Architecture

5.1 Front-end

5.2 Back-end

5.3 User Interface

5.4 Gnuplot Interface

5.5 Execution Engine

Chapter 6: Plotting

6.1 Simple Function Plot (fplot)

6.2 Two-Dimensional Plots

6.3 Three-Dimensional Plots

Part II

Chapter 7: Solving Nonlinear Equations

7.1 Calculation of Roots with the use of Iterative Functions

7.2 Exercises

Chapter 8: Solving Systems of Linear Equations

8.1 Linear Algebra Background

8.2 Systems of Linear Equations

8.3 Types of Matrices that arise from Applications and Analysis

8.4 Error Sources

8.5 Condition Number

8.6 Direct Methods

8.7 Iterative Methods

8.8 Exercises

Chapter 9: Computational Eigenvalue Problems

9.1 Basic Facts concerning Eigenvalue Problems

9.2 Localization of Eigenvalues

9.3 Power Method

9.4 Inverse Iteration

9.5 Iteration with a Shift of Origin

9.6 The QR Method

9.7 Exercises

Chapter 10: Introduction to Finite Difference Schemes for Ordinary Differential Equations

10.1 Elementary Example

Details

No. of pages:
208
Language:
English
Copyright:
© 2011
Published:
Imprint:
Woodhead Publishing
eBook ISBN:
9780857092267
Print ISBN:
9780857092250
Print ISBN:
9781904275466

About the authors

Victor Zalizniak

Dr. Victor Zalizniak was awarded his Masters in Physics at Krasnoyarsk State University, Russia before becoming a Research Fellow at the Centre for Scientific Computing at the Russian Academy of Sciences (Siberian Branch). He then moved to the Department of Aerospace Engineering at the Royal Melbourne Institute of Technology where he obtained his PhD. In 2001 he returned to the Department of Computer Science at his alma mater, Krasnoyarsk State University, where he continues to lecture, research and write in his particular fields of computational physics and mathematical physics. He is the author of several books on scientific computing including Essentials of Computational Physics Parts 1 and 2.

Affiliations and Expertise

Siberian Federal University, Russia