## Introduction to Numerical AnalysisAn Introduction to Numerical Analysis is designed for a first course on numerical analysis for students of Science and Engineering including Computer Science. The text contains derivation of algorithms for solving engineering and science problems and also deals with error analysis. It has numerical examples suitable for solving through computers. The special features are comparative efficiency and accuracy of various algorithms due to finite digit arithmetic used by the computers. |

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### Contents

Finite Digit Arithmetic and Errors | 1 |

Nonlinear Equations | 12 |

System of Linear Equations | 48 |

Exercises Set 3 | 87 |

Exercises Set 4 | 119 |

Exercises Set 5 | 178 |

Eigenvalues and Eigenvectors | 220 |

Partial Differential Equations | 280 |

136 | 286 |

Boundary Value Problems | 317 |

References | 346 |

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### Common terms and phrases

algorithm analytic solution approximate arithmetic with rounding boundary conditions boundary value problem column composite Simpson's composite Trapezoidal rule compute corresponding eigenvector denoted difference equation digit arithmetic eigen eigenvalues and corresponding eigenvalues and eigenvectors error term Euler's method Evaluate the integral Example find the eigenvalues finite digit fprintf(fp,"\nThe Gauss-elimination Gauss-Seidel Hence initial conditions initial value problems interpolating polynomial iteration function Iteration number Jacobi's method linear combination matrix A*V mesh points method converges method of order method to find multipliers Newton's method numerically largest eigenvalue obtained order Runge-Kutta method orthogonal matrix pair partial differential equations pn(x polynomial of degree predictor-corrector QR Algorithm Quadrature root Runge-Kutta method secant method sequence Simpson's rule solving spacing h starting vector subtraction Suppose symmetric matrix system of equations Table tabular points Taylor's series temperature distribution transformation Trapezoidal rule true solution yn+i zero