## Numerical Analysis for Applied ScienceWritten for graduate students in applied mathematics, engineering and science courses, the purpose of this book is to present topics in "Numerical Analysis" and "Numerical Methods." It will combine the material of both these areas as well as special topics in modern applications. Included at the end of each chapter are a variety of theoretical and computational exercises. |

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### Contents

Some Useful Tools | 1 |

Approximation of Functions | 27 |

Direct Methods for Linear Systems | 109 |

Solution of Nonlinear Equations | 161 |

Iterative Methods for Linear Systems | 221 |

Eigenvalue Problems | 283 |

Numerical Integration | 313 |

Ordinary Differential Equations | 349 |

Difference Methods for PDEs | 395 |

Introduction to Finite Elements | 447 |

Divided Differences | 477 |

Chebyshev Polynomials | 483 |

### Common terms and phrases

algorithm analog apply associated basis functions bounded Chapter coefficients compute condition consider constant COROLLARY cubic defined denote derivatives diagonal entries difference differential discuss eigenvalues eigenvectors Equation error estimate example exists explicit fact Figure finite Fourier Gauss Gauss-Seidel Gauss-Seidel method graph grid function heat equation implies induction initial guess inner product inner-product space integral interval iterative scheme Jacobi method Lemma linear system linearly Lipschitz LU factorization magnitude matrix norm mesh size h Mnxn multiplicity multistep methods multistep scheme Newton-Cotes formulas Newton's method nodes nonsingular nonzero one-step method orthogonal permutation permutation matrix pivoting polynomial interpolation positive definite problem PROOF PROPOSITION prove QR decomposition quadrature requires row reduction satisfies secant method Section sequence solve spline stepsize subinterval successive substitution symmetric and positive theorem tion triangle inequality tridiagonal truncation error upper triangular vanishes vector space yields zero