## FIRST PRINCIPLES OF NUMERICAL ANALYSIS: AN UNDERGRADUATE TEXT. |

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### Contents

Applications of Taylors Theorem Part 1 | 19 |

Applications of Taylors Theorem Part 2 | 33 |

The Theory of Interpolation | 55 |

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