## First principles of numerical analysis: an undergraduate text |

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### Contents

Applications of Taylors Theorem Part 1 | 17 |

Applications of Taylors Theorem Part 2 | 33 |

The Theory of Interpolation | 55 |

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algorithm approximation arithmetic operations arithmetic unit assume called Chapter coefficients compute continuous convergence cubic defined derivatives difference quotient distinct points error Euler's method example EXERCISES Section false position Fetch finite fixed floating binary flow diagram formula function f(x functional evaluations Gaussian elimination Gaussian quadrature given Hermite interpolation Heun's method induction integration rule interchange interpolating function interpolating spline interval iteration Jy-h Lagrange interpolating polynomial Lemma Let P(x linear system machine method of false multi-point methods multiplicity Newton's method nodes numerical analysis obtained orthogonal partial pivoting pk(x polynomial interpolation polynomial of degree polynomial P(x powers of h problem Proof rectangle rule replace result Richardson extrapolation roots satisfies sequence set of numbers Simpson's rule single step methods solution solve stored program Suppose Taylor's theorem tion trapezoidal rule triangular decomposition vanishes Wendroff xi+1 Yn+1 zero