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Numerical Methods in Engineering with Python 3, Third Edition

Book Description

This book is an introduction to numerical methods for students in engineering. It covers solution of equations, interpolation and data fitting, solution of differential equations, eigenvalue problems and optimisation. The algorithms are implemented in Python 3, a high-level programming language that rivals MATLAB® in readability and ease of use. All methods include programs showing how the computer code is utilised in the solution of problems. The book is based on Numerical Methods in Engineering with Python, which used Python 2. This new edition demonstrates the use of Python 3 and includes an introduction to the Python plotting package Matplotlib. This comprehensive book is enhanced by the addition of numerous examples and problems throughout.

Table of Contents

  1. Cover
  2. Numerical Methods in Engineering with Python 3
  3. Title Page
  4. Copyright
  5. Table of Contents
  6. Preface
  7. 1 Introduction to Python
    1. 1.1 General Information
    2. 1.2 Core Python
    3. 1.3 Functions and Modules
    4. 1.4 Mathematics Modules
    5. 1.5 numpy Module
    6. 1.6 Plotting with matplotlib.pyplot
    7. 1.7 Scoping of Variables
    8. 1.8 Writing and Running Programs
  8. 2 Systems of Linear Algebraic Equations
    1. 2.1 Introduction
    2. 2.2 Gauss Elimination Method
    3. 2.3 LU Decomposition Methods
    4. Problem Set 2.1
    5. 2.4 Symmetric and Banded Coefficient Matrices
    6. 2.5 Pivoting
    7. Problem Set 2.2
    8. *2.6 Matrix Inversion
    9. *2.7 Iterative Methods
    10. Problem Set 2.3
    11. 2.8 Other Methods
  9. 3 Interpolation and Curve Fitting
    1. 3.1 Introduction
    2. 3.2 Polynomial Interpolation
    3. 3.3 Interpolation with Cubic Spline
    4. Problem Set 3.1
    5. 3.4 Least-Squares Fit
    6. Problem Set 3.2
  10. 4 Roots of Equations
    1. 4.1 Introduction
    2. 4.2 Incremental Search Method
    3. 4.3 Method of Bisection
    4. 4.4 Methods Based on Linear Interpolation
    5. 4.5 Newton-Raphson Method
    6. 4.6 Systems of Equations
    7. Problem Set 4.1
    8. *4.7 Zeros of Polynomials
    9. Problem Set 4.2
    10. 4.8 Other Methods
  11. 5 Numerical Differentiation
    1. 5.1 Introduction
    2. 5.2 Finite Difference Approximations
    3. 5.3 Richardson Extrapolation
    4. 5.4 Derivatives by Interpolation
    5. Problem Set 5.1
  12. 6 Numerical Integration
    1. 6.1 Introduction
    2. 6.2 Newton-Cotes Formulas
    3. 6.3 Romberg Integration
    4. Problem Set 6.1
    5. 6.4 Gaussian Integration
    6. Problem Set 6.2
    7. *6.5 Multiple Integrals
    8. Problem Set 6.3
  13. 7 Initial Value Problems
    1. 7.1 Introduction
    2. 7.2 Euler’s Method
    3. 7.3 Runge-Kutta Methods
    4. Problem Set 7.1
    5. 7.4 Stability and Stiffness
    6. 7.5 Adaptive Runge-Kutta Method
    7. 7.6 Bulirsch-Stoer Method
    8. Problem Set 7.2
    9. 7.7 Other Methods
  14. 8 Two-Point Boundary Value Problems
    1. 8.1 Introduction
    2. 8.2 Shooting Method
    3. Problem Set 8.1
    4. 8.3 Finite Difference Method
    5. Problem Set 8.2
  15. 9 Symmetric Matrix Eigenvalue Problems
    1. 9.1 Introduction
    2. 9.2 Jacobi Method
    3. 9.3 Power and Inverse Power Methods
    4. Problem Set 9.1
    5. 9.4 Householder Reduction to Tridiagonal Form
    6. 9.5 Eigenvalues of Symmetric Tridiagonal Matrices
    7. Problem Set 9.2
    8. 9.6 Other Methods
  16. 10 Introduction to Optimization
    1. 10.1 Introduction
    2. 10.2 Minimization Along a Line
    3. 10.3 Powell’s Method
    4. 10.4 Downhill Simplex Method
    5. Problem Set 10.1
  17. Appendices
    1. A1 Taylor Series
    2. A2 Matrix Algebra
  18. List of Program Modules (by Chapter)
  19. Index