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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.
- 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
Professionals and academics.
Chapter 1: Introduction
1.1 Getting Started
Chapter 2: Expressions
2.2 Real Number
2.3 Complex Number
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
4.4 Java Programming
4.5 C Programming
Chapter 5: Architecture
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
Chapter 7: Solving Nonlinear Equations
7.1 Calculation of Roots with the use of Iterative Functions
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
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
Chapter 10: Introduction to Finite Difference Schemes for Ordinary Differential Equations
10.1 Elementary Example of a Finite Difference Scheme
10.2 Approximation and Stability
10.3 Numerical Solution of Initial Value Problems
10.4 Numerical Solution of Boundary Value Problems
10.5 Error Estimation and Control
Chapter 11: Interpolation and Approximation
11.2 Approximation of Functions and Data Representation
- No. of pages:
- © Woodhead Publishing 2011
- 26th February 2011
- Woodhead Publishing
- Paperback ISBN:
- Paperback ISBN:
- eBook ISBN:
Professor of Biotechnology, Vice Chancellor, Government College University, Faisalabad, Pakistan
Government College University, Faisalabad, Pakistan; Health biotechnology, molecular biology, biomaterials
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.
Siberian Federal University, Russia
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