An Introduction to Numerical Methods: A MATLAB Approach / Edition 2

An Introduction to Numerical Methods: A MATLAB Approach / Edition 2

by Abdelwahab Kharab, Ronald B. Guenther
     
 

Numerical methods are a mainstay of researchers and professionals across the many mathematics, scientific, and engineering disciplines. The importance of these methods combined with the power and availability of today's computers virtually demand that students in these fields be well versed not only in the numerical techniques, but also in the use of a modern

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Overview

Numerical methods are a mainstay of researchers and professionals across the many mathematics, scientific, and engineering disciplines. The importance of these methods combined with the power and availability of today's computers virtually demand that students in these fields be well versed not only in the numerical techniques, but also in the use of a modern computational software package.

Updated to reflect the latest version of MATLAB, the second edition of An Introduction to Numerical Methods continues to fulfill both these needs. It introduces the theory and applications of the most commonly used techniques for solving numerical problems on a computer. It covers a wide range of useful algorithms, each presented with full details so that readers can visualize and interpret each step.

Highlights of the second edition:

  • A new chapter on numerical optimization
  • New sections on finite elements
  • More exercises and applied problems in each chapter
  • MATLAB incorporated as an integral part of the text

    Emphasis on understanding how the methods work, a simple, direct style, and thorough coverage make this book an outstanding initiation that allows students to see almost immediate results. It will boost their confidence in their ability to master the subject and give them valuable experience in the use of MATLAB.

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    Product Details

    ISBN-13:
    9781584885573
    Publisher:
    Taylor & Francis
    Publication date:
    07/28/2005
    Edition description:
    REV
    Pages:
    624
    Product dimensions:
    6.20(w) x 9.30(h) x 1.50(d)

    Table of Contents

    INTRODUCTION
    About the software MATLAB
    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
    SYSTEM OF LINEAR EQUATIONS
    Matrices and Matrix Operations
    Naïve Gaussian Elimination
    Gaussian Elimination with Scaled Partial Pivoting
    LU Decomposition
    Iterative Methods
    INTERPOLATION
    Polynomial Interpolation Theory
    Newton's Divided Difference Interpolating Polynomial
    The Error of the Interpolating Polynomial
    Lagrange Interpolating Polynomial
    INTERPOLATION WITH SPLINE FUNCTIONS
    Piecewise Linear Interpolation
    Quadratic Spline
    Natural Cubic Splines
    THE METHOD OF LEAST SQUARES
    Linear Least Squares
    Least Squares Polynomial
    Nonlinear Least Squares
    Trigonometric Least Squares Polynomial
    NUMERICAL OPTIMIZATION
    Analysis of Single-Variable Functions
    Line Search Methods
    Minimization Using Derivatives
    NUMERICAL DIFFERENTIATION
    Numerical Differentiation
    Richardson's Formula
    NUMERICAL INTEGRATION
    Trapezoidal Rule
    Simpson's Rule
    Romberg Algorithm
    Gaussian Quadrature
    NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS
    Euler's Method
    Error Analysis
    Higher Order Taylor Series Methods
    Runge-Kutta Methods
    Multistep Methods
    Adams-Bashforth Method
    Predictor-Corrector Methods
    Adams-Moulton Method
    Numerical Stability
    Higher Order Equations and Systems of Differential Equations
    Implicit Methods and Stiff Systems
    Phase Plane Analysis: Chaotic Differential Equations
    BOUNDARY-VALUE PROBLEMS
    Finite-Difference Methods
    Shooting Methods
    EIGENVALUES AND EIGENVECTORS
    Basic Theory
    The Power Method
    The Quadratic Method
    Eigenvalues for Boundary-Value Problems
    Bifurcations in Differential Equations
    PARTIAL DIFFERENTIAL EQUATIONS
    Parabolic Equations
    Hyperbolic Equations
    Elliptic Equations
    Introduction to Finite Element Method
    Bibliography and References
    Appendices
    Calculus Review
    MATLAB Built-in Functions
    Text MATLAB Functions
    Answers to Selected Exercises
    Index

    Each chapter also contains a section of Applied Problems.

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