## Numerical Analysis II EssentialsCovers simultaneous linear systems and matrix methods, differential equations, Fourier transformations, partial differential equations, and Monte Carlo methods. |

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### Contents

I | 82 |

II | 87 |

III | 90 |

IV | 91 |

V | 93 |

VI | 101 |

VII | 108 |

VIII | 110 |

XIII | 125 |

XIV | 128 |

XV | 131 |

XVI | 140 |

XVII | 145 |

XVIII | 148 |

XIX | 150 |

XX | 153 |

### Common terms and phrases

Adams-Bashforth associated eigenvector augmented matrix boundary value problem characteristic polynomial column computed cosine series defined Definition denoted det(A difference equation dominant eigenvalue eigenvalues eigenvector exist explicit method f converges f is piecewise finite difference method following theorem Fourier cosine series Fourier sine series Fourier transform function f Gauss-Seidel method given h f(x)cos hf(x initial approximation initial conditions initial value problem integral iterative linear system Lipschitz condition matrix form mesh points method applied Monte Carlo methods multistep method non-singular norm NUMERICAL ANALYSIS numerical method Parseval's identity PARTIAL DIFFERENTIAL EQUATION period 2h periodic with period pivot element power method predictor predictor-corrector methods pseudorandom numbers random numbers rectangularly distributed reduce round off error Runge-Kutta method satisfies a Lipschitz sequence series of f set h solve SOR method starting values Taylor Taylor's method trigonometric Fourier Series truncation error vector x e a,b x e h,h yi+i zero