Cheney, Ward. creator Kincaid, Ward. text xxu Bonn Brooks/Cole publishing 1999 4 ed. monographic eng

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xv,671 p.: ill.; 24cm. Contents: Introduction: Preliminary remarks -- Programming suggestions -- Review of Taylor series -- Number representation and errors: Representation of numbers in diferent bases -- Floating-point representation -- Loss of significance -- Locating roots of equations: Bisection method -- Newton's method -- Secant method -- Interpolation and numerical differentiation: Preliminary remarks -- Polynomial interpolation -- Errors in polynomial interpolation -- Estimating derivatives and Richardson extrapolation -- Numerical integration -- Definite integral -- Trapezoid rule -- Romberg algorithm -- An Adaptive Simpson's scheme -- Gaussian quadrature formulas -- Systems of linear equations: Naive gaussian elimination -- Gaussian elimination with scaled partial pivoting -- Tridiagonal and banded systems -- LU factorization -- Iterative solution of linear equations -- Approximation by spline functions: Introduction -- First-degree and second-degree splines -- Natural cubic splines -- B splines -- Interpolation and approximation B splines -- Ordinary differential equations: Initial-value problem: Analytical vs. numerical solution -- Taylor series methods -- Runge-Kutta methods -- Stability and adaptive Runge-Kutta and multi-step methods -- Systems of ordinary differential equations -- Higher-order equations and systems -- Adams-Moulton methods -- Smoothing of data and the method of least squares: The Method of least squares -- Orthogonal systems and chebyshev polynomials -- Other examples of the least-squares principle -- Monte Carlo methods and simulation: Random numbers -- Estimation of areas and volumes by Monte Carlo techniques -- Simulation -- Boundary value problems for ordinary differential equations: Preliminary remaks -- Shooting method -- A Discretization method -- Partial differential equations: Introduction -- Parabolic problems -- Hyperbolic problems -- Elliptic problems -- Minimization of multivariante functions: Inteduction -- One-variable case -- Multivariate case -- Linear programming: Standard forms and duality -- Simple method -- Approximate solution of inconsistent linear systems -- Appendix A: Linear algebra concepts and notation: Elemetary concepts -- Abstract vector spaces -- Appendix B: Mathematical software. Ward Cheney and David Kincaid Includes bibliographical references and index. QA276.C41 0534351840 120709