## Applied Numerical Methods Using MATLABIn recent years, with the introduction of new media products, there has been a shift in the use of programming languages from FORTRAN or C to MATLAB for implementing numerical methods. This book makes use of the powerful MATLAB software to avoid complex derivations, and to teach the fundamental concepts using the software to solve practical problems. Over the years, many textbooks have been written on the subject of numerical methods. Based on their course experience, the authors use a more practical approach and link every method to real engineering and/or science problems. The main benefit is that engineers don't have to know the mathematical theory in order to apply the numerical methods for solving their real-life problems. An Instructor's Manual presenting detailed solutions to all the problems in the book is available online. |

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### Contents

1 | |

2 System of Linear Equations | 71 |

3 Interpolation and Curve Fitting | 117 |

4 Nonlinear Equations | 179 |

5 Numerical DifferentiationIntegration | 209 |

6 Ordinary Differential Equations | 263 |

7 Optimization | 321 |

8 Matrices and Eigenvalues | 371 |

Appendix D Laplace Transform | 473 |

Appendix E Fourier Transform | 475 |

Appendix F Useful Formulas | 477 |

Appendix G Symbolic Computation | 481 |

Appendix H Sparse Matrices | 489 |

Appendix I MATLAB | 491 |

497 | |

499 | |

9 Partial Differential Equations | 401 |

Appendix A Mean Value Theorem | 461 |

Appendix B Matrix OperationsProperties | 463 |

Appendix C Differentiation with Respect to a Vector | 471 |

503 | |

Index for Tables | 509 |

### Other editions - View all

Applied Numerical Methods Using MATLAB Won Y. Yang,Wenwu Cao,Tae-Sang Chung,John Morris No preview available - 2005 |

### Common terms and phrases

algorithm apply axis bisection method boundary condition button Chebyshev Chebyshev nodes clicking coefﬁcient computation constraints converge curve data points deﬁned depicted in Fig derivative diagonal dialog box difference approximation differential equation eigenvalues eigenvectors element end end Example Figure ﬁnd ﬁrst flops fmincon formula function f graph grid points initial condition initial guess initial value input argument integration interpolation interval inverse iteration kmax Lagrange polynomial linear equations LU decomposition M-file MATLAB built-in routine MATLAB command window MATLAB program MATLAB routine MaxIter mesh minimization minimum nargin Neumann boundary condition Newton method Newton polynomial nodes nonlinear equations Note Numerical Methods numerical solution objective function obtained optimization parameters partial pivoting PDEtool plot polynomial problem pull-down menu result Section segments solve step-size subintervals Table Taylor series TolFun TolX typing the following variable vector xk+1 zero