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    Applied Numerical Analysis

    ISBN-10: 032119019X
    ISBN-13: 9780321190192
    Author(s): Curtis F Gerald
    Description: Incorporating a balance of theory with techniques and applications, this text includes optional theory-based sections. The topics, such as partial differential equations and matrix algebra, provide comprehensive and flexible coverage of all aspects  More...
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    Publisher: PEARSON HIGHER EDUCATION
    Binding: Paperback
    Size: 7.60" wide x 9.09" long x 1.14" tall
    Weight: 2.090

    Incorporating a balance of theory with techniques and applications, this text includes optional theory-based sections. The topics, such as partial differential equations and matrix algebra, provide comprehensive and flexible coverage of all aspects of numerical analysis.

    Preliminaries
    Analysis versus Numerical Analysis
    Computers and Numerical Analysis
    An Illustrative Example
    Kinds of Errors in Numerical Procedures
    Interval Arithmetic
    Parallel and Distributed Computing
    Measuring the Efficiency of Procedures
    Solving Nonlinear Equations
    Interval Halving (Bisection)
    Linear Interpolation Methods
    Newton's Method
    Muller's Method
    Fixed-Point Iteration
    Other Methods
    Nonlinear Systems
    Solving Sets of Equations
    Matrices and Vectors
    Elimination Methods
    The Inverse of a Matrix and Matrix Pathology
    Almost Singular Matrices - Condition Numbers
    Interactive Methods
    Parallel Processing
    Interpolation and Curve Fitting
    Interpolating Polynomials
    Divided Differences
    Spline Curves
    Bezier Curves and B-Splines
    Interpolating on a Surface
    Least Squares Approximations
    Approximation of Functions
    Chebyshev Polynomials and Chebyshev Series
    Rational Function Approximations
    Fourier Series
    Numerical Differentiation and Integration
    Differentiation with a Computer
    Numerical Integration - The Trapezoidal Rule
    Simpson's Rules
    An Application of Numerical Integration - Fourier Series and Fourier Transforms Adaptive Integration
    Gaussian Quadrature
    Multiple Integrals
    Applications of Cubic Splines
    Numerical Solution of Ordinary Differential Equations
    The Taylor Series Method
    The Euler Method and Its Modification
    Runge-Kutta Methods
    Multistep Methods
    Higher-Order Equations and Systems
    Stiff Equations
    Boundary-Value Problems
    Characteristic-Value Problems
    Optimization
    Finding the Minimum of y = f(x)
    Minimizing a Function of Several Variables
    Linear Programming
    Nonlinear Programming
    Other Optimizations
    Partial Differential Equations
    Elliptic Equations
    Parabolic Equations
    Hyperbolic Equations
    Finite Element Analysis
    Mathematical Background
    Finite Elements for Ordinary Differential Equation
    Finite Elements for Partial Differential Equation
    Appendices
    Some Basic Information from Calculus
    Software Resources
    Answers to Selected Exercises
    References
    Index

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