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## Details

Genre/Form: | Electronic books |
---|---|

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Abdelwahab Kharab; Ronald B Guenther |

ISBN: | 9781439869000 1439869006 |

OCLC Number: | 1024080448 |

Description: | 1 online resource |

Contents: | Introduction; About MATLAB and MATLAB graphical user interface (GUI); An introduction to MATLAB; Taylor series Number System and Errors ; Floating-point arithmetic; Round-off errors; Truncation error; Interval arithmetic Roots of Equations ; The bisection method; The method of false position; Fixed-point iteration; The secant method; Newton's method; Convergence of the Newton and Secant methods; Multiple roots and the modified Newton method; Newton's method for nonlinear systems; Applied problems System of Linear Equations ; Matrices and matrix operations; Naïve Gaussian elimination; Gaussian elimination with scaled partial pivoting; Lu decomposition; Iterative methods; Applied problems Interpolation; Polynomial interpolation theory; Newton's divided-difference interpolating polynomial; The. Error of the interpolating polynomial; Lagrange interpolating polynomial; Applied problems Interpolation with Spline Functions ; Piecewise linear interpolation; Quadratic spline; Natural cubic splines; Applied problems The Method of Least Squares ; Linear least squares; Least-squares polynomial; Nonlinear least squares; Trigonometric least-squares polynomial; Applied problems Numerical Optimization ; Analysis of single-variable functions; Line search methods; Minimization using derivatives; Applied problems Numerical Differentiation ; Numerical differentiation; Richardson's formula; Applied problems Numerical Integration; Trapezoidal rule; Simpson's rule; Romberg algorithm; Gaussian quadrature; Applied problems Numerical Methods for Linear Integral. Equations ; Introduction; Quadrature rules; The successive approximation method; Schmidt's method; Volterra-type integral equations; Applied problems Numerical Methods for Differential Equations ; Euler's Method; Error Analysis; Higher-order Taylor series methods; Runge-Kutta methods; Adams-Bashforth methods; Predictor-corrector methods; Adams-Moulton methods; Numerical stability; Higher-order equations and systems of differential equations; Implicit methods and stiff systems; Phase plane analysis: chaotic differential equations; Applied problems Boundary-Value Problems; Finite-difference methods; Shooting methods; Applied problems Eigenvalues and Eigenvectors ; Basic theory; The power method; The quadratic method; Eigenvalues for boundary-value problems; Bifurcations in differential equations; Applied. Problems Partial Differential Equations; Parabolic equations; Hyperbolic equations; Elliptic equations; Nonlinear partial differential equations; Introduction to finite-element method; Applied problems Bibliography and References Appendix A: Calculus Review; Appendix B: MATLAB Built-in Functions; Appendix C: Text MATLAB Functions; Appendix D: MATLAB GUI Answers to Selected Exercises Index. |

Responsibility: | Abdelwahab Kharab, Ronald B. Guenther. |

### Abstract:

Introduces the theory and applications of the most commonly used techniques for solving numerical problems on a computer. This work covers a range of useful algorithms. It includes a chapter on numerical optimization. It also features sections on finite elements.
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## Reviews

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Publisher Synopsis

Praise for Previous EditionsKharab and Guenther offer an attractive, clear, error-free, and well-written introduction to numerical methods ... Highly recommended.-J.H. Ellison, CHOICE

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