An Introduction to Numerical Methods: A MATLAB Approach / Edition 1

An Introduction to Numerical Methods: A MATLAB Approach / Edition 1

by Abdelwahab Kharab, Ronald B. Guenther
     
 

ISBN-10: 1584882816

ISBN-13: 9781584882817

Pub. Date: 01/28/2002

Publisher: Taylor & Francis

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

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.

  • Product Details

    ISBN-13:
    9781584882817
    Publisher:
    Taylor & Francis
    Publication date:
    01/28/2002
    Edition description:
    Older Edition
    Pages:
    448
    Product dimensions:
    6.30(w) x 9.44(h) x 1.17(d)

    Related Subjects

    Table of Contents

    1Introduction1
    1.1About the Software Matlab1
    1.2An Introduction to Matlab2
    1.2.1Matrices and matrix computation2
    1.2.2Output format6
    1.2.3Planar plots7
    1.2.43-D mesh plots8
    1.2.5Function files9
    1.2.6Defining functions10
    1.2.7Relations and loops11
    1.3Taylor Series13
    2Number System and Errors21
    2.1Floating-Point Arithmetic21
    2.2Round-off Errors26
    2.3Truncation Error29
    2.4Interval Arithmetic30
    3Roots of Equations37
    3.1The Bisection Method37
    3.2The Method of False Position44
    3.3The Secant Method48
    3.4Newton's Method52
    3.5Convergence of the Newton and Secant Methods58
    3.6Fixed Point Iteration60
    3.7Multiple Roots and the Modified Newton Method66
    3.8Newton's Method for Nonlinear Systems72
    4System of Linear Equations79
    4.1Matrices and Matrix Operations79
    4.2Naive Gaussian Elimination83
    4.3Gaussian Elimination with Scaled Partial Pivoting92
    4.4Lu Decomposition102
    4.4.1Crout's and Choleski's methods102
    4.4.2Gaussian elimination method108
    4.5Iterative Methods115
    4.5.1Jacobi iterative method115
    4.5.2Gauss-Seidel iterative method119
    4.5.3Convergence123
    5Interpolation131
    5.1Polynomial Interpolation Theory132
    5.2Newton's Divided Difference Interpolating Polynomial134
    5.3The Error of the Interpolating Polynomial144
    5.4Lagrange Interpolating Polynomial147
    6Interpolation with Spline Functions153
    6.1Piecewise Linear Interpolation153
    6.2Quadratic Spline158
    6.3Natural Cubic Splines161
    7The Method of Least Squares175
    7.1Linear Least Squares176
    7.2Least Squares Polynomial182
    7.3Nonlinear Least Squares190
    7.3.1Exponential form191
    7.3.2Hyperbolic form193
    7.4Trigonometric Least Squares Polynomial197
    8Numerical Differentiation and Integration203
    8.1Numerical Differentiation204
    8.2Richardson's Formula208
    8.3Trapezoidal Rule214
    8.4Simpson's Rule222
    8.5Romberg Algorithm230
    8.6Gaussian Quadrature237
    9Numerical Methods for Ordinary Differential Equations247
    9.1Euler's Method247
    9.2Error Analysis254
    9.3Higher Order Taylor Series Methods259
    9.4Runge-Kutta Methods262
    9.5Multistep Methods272
    9.6Adams-Bashforth Method273
    9.7Predictor-Corrector Methods282
    9.8Adams-Moulton Method283
    9.9Numerical Stability289
    9.10Higher Order Equations and Systems292
    9.11Implicit Methods and Stiff Systems299
    9.12Phase Plane Analysis: Chaotic Equations301
    10Boundary-Value Problems311
    10.1Finite-Difference Methods311
    10.2Shooting Methods318
    10.2.1The nonlinear case318
    10.2.2The linear case321
    11Eigenvalues and Eigenvectors329
    11.1Basic Theory329
    11.2The Power Method334
    11.3The Quadratic Method338
    11.4Eigenvalues for Boundary-Value Problems349
    11.5Bifurcations in Differential Equations352
    12Partial Differential Equations359
    12.1Parabolic Equations360
    12.1.1Explicit methods360
    12.1.2Implicit methods366
    12.2Hyperbolic Equations373
    12.3Elliptic Equations380
    Bibliography and References389
    Appendix ACalculus Review393
    A.0.1Limits and continuity393
    A.0.2Differentiation394
    A.0.3Integration394
    Appendix BMatlab Built-In Functions397
    Appendix CText Matlab Functions401
    Answers to Selected Exercises403
    Index427

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