## Numerical Methods in Engineering with PythonNumerical Methods in Engineering with Python is a text for engineering students and a reference for practicing engineers, especially those who wish to explore the power and efficiency of Python. Examples and applications were chosen for their relevance to real world problems, and where numerical solutions are most efficient. Numerical methods are discussed thoroughly and illustrated with problems involving both hand computation and programming. Computer code accompanies each method and is available on the book web site. This code is made simple and easy to understand by avoiding complex bookkeeping schemes, while maintaining the essential features of the method. Python was chosen as the example language because it is elegant, easy to learn and debug, and its facilities for handling arrays are unsurpassed. Moreover, it is an open-source software package; free and available to all students and engineers. Explore numerical methods with Python, a great language for teaching scientific computation. |

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### Contents

Introduction to Python | 1 |

Systems of Linear Algebraic Equations | 27 |

Interpolation and Curve Fitting | 103 |

Roots of Equations | 142 |

Numerical Differentiation | 181 |

Numerical Integration | 198 |

Initial Value Problems | 248 |

TwoPoint Boundary Value Problems | 295 |

Symmetric Matrix Eigenvalue Problems | 324 |

Introduction to Optimization | 381 |

Appendices | 409 |

### Common terms and phrases

algorithm back substitution bisection boundary conditions boundary value problem bracketed Brent's method Choleski's decomposition column compute constant vector constraints convergence cubic spline data points decimal places derivatives Determine diagonal differential equation displacement Doolittle's decomposition eigenvalue problem eigenvectors elements equations Ax evaluate EXAMPLE finite difference approximations Gauss elimination Gauss-Legendre quadrature Gauss-Seidel method initial conditions initial value problem interval inverse power method Jacobi method linear listed loop LU decomposition LUdecompS math import sqrt minimizes module Newton-Raphson method nodes numarray import array number of iterations numerical integration optimization output panels plot polynomial interpolation Press return Prob PROBLEM SET procedure Python quadratic quadrilateral range(n raw_input(''\nPress return return to exit Richardson extrapolation Romberg integration root roundoff error Runge-Kutta method shown solution Solve the equations symmetric Table Taylor series trapezoidal rule tridiagonal truncation error usr/bin/python variables Write a program xStop yields zero