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Practical Scientific Computing

Book 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 MATLABĀ®. 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

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Preface
  6. Acknowledgements
  7. Part I
    1. Chapter 1: Introduction
      1. 1.1 Getting Started
      2. 1.2 Interpreter
      3. 1.3 Program
    2. Chapter 2: Expressions
      1. 2.1 Matrix
      2. 2.2 Real Number
      3. 2.3 Complex Number
      4. 2.4 Boolean
      5. 2.5 String
      6. 2.6 Structure
      7. 2.7 Cell
      8. 2.8 Range Expression
      9. 2.9 Boolean Expression
      10. 2.10 Relational Expression
      11. 2.11 Numerical Expression
    3. Chapter 3: Statements
      1. 3.1 Assignment Statement
      2. 3.2 Loop Statements
      3. 3.3 Conditional Statements
      4. 3.4 Continue and Break Statements
    4. Chapter 4: Programming
      1. 4.1 Program
      2. 4.2 Function
      3. 4.3 Procedure
      4. 4.4 Java Programming
      5. 4.5 C Programming
    5. Chapter 5: Architecture
      1. 5.1 Front-end
      2. 5.2 Back-end
      3. 5.3 User Interface
      4. 5.4 Gnuplot Interface
      5. 5.5 Execution Engine
    6. Chapter 6: Plotting
      1. 6.1 Simple Function Plot (fplot)
      2. 6.2 Two-Dimensional Plots
      3. 6.3 Three-Dimensional Plots
  8. Part II
    1. Chapter 7: Solving Nonlinear Equations
      1. 7.1 Calculation of Roots with the use of Iterative Functions
      2. 7.2 Exercises
    2. Chapter 8: Solving Systems of Linear Equations
      1. 8.1 Linear Algebra Background
      2. 8.2 Systems of Linear Equations
      3. 8.3 Types of Matrices that arise from Applications and Analysis
      4. 8.4 Error Sources
      5. 8.5 Condition Number
      6. 8.6 Direct Methods
      7. 8.7 Iterative Methods
      8. 8.8 Exercises
    3. Chapter 9: Computational Eigenvalue Problems
      1. 9.1 Basic Facts concerning Eigenvalue Problems
      2. 9.2 Localization of Eigenvalues
      3. 9.3 Power Method
      4. 9.4 Inverse Iteration
      5. 9.5 Iteration with a Shift of Origin
      6. 9.6 The QR Method
      7. 9.7 Exercises
    4. Chapter 10: Introduction to Finite Difference Schemes for Ordinary Differential Equations
      1. 10.1 Elementary Example of a Finite Difference Scheme
      2. 10.2 Approximation and Stability
      3. 10.3 Numerical Solution of Initial Value Problems
      4. 10.4 Numerical Solution of Boundary Value Problems
      5. 10.5 Error Estimation and Control
      6. 10.6 Exercises
    5. Chapter 11: Interpolation and Approximation
      1. 11.1 Interpolation
      2. 11.2 Approximation of Functions and Data Representation
      3. 11.3 Exercises
  9. Bibliography