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Applied Numerical Analysis Using MATLAB
£73.99

APPLIED NUMERICAL ANALYSIS USING MATLAB

HARDBACK BY FAUSETT, LAURENE V.

£73.99

ISBN
9780132397285
IMPRINT
PEARSON
 
 
EDITION
2ND EDITION
PUBLISHER
PEARSON EDUCATION (US)
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FORMAT
HARDBACK
PAGES
688 pages
PUBLICATION DATE
01 MAR 2007

DESCRIPTION

This text is appropriate for undergraduate courses on numerical methods and numerical analysis found in engineering, mathematics & computer science departments. Each chapter uses introductory problems from specific applications. These easy-to-understand problems clarify for the reader the need for a particular mathematical technique. Numerical techniques are explained with an emphasis on why they work.

CONTENTS

Contents Preface 1 Foundations 11.1 Introductory Examples 1.1.1 Nonlinear Equations 1.1.2 Linear Systems 1.1.3 Numerical Integration 1.2 Useful Background 1.2.1 Results from Calculus 1.2.2 Results from Linear Algebra 1.2.3 A Little Information1.3.1 Error 1.3.2 Convergence 1.3.3 Getting Better Results 1.4 Using MATLAB 1.4.1 Command Window Computations 1.4.2 M-Files 1.4.3 Programming in MATLAB 1.4.4 Matrix Multiplication 1.5 Chapter Wrap-Up 2 Functions of One Variable 472.1 Bisection Method 2.2 Secant-Type Methods 2.2.1 Regula Falsi 2.2.2 Secant Method 2.2.3 Analysis 2.3 Newton's Method2.4 Muller's Method 2.5 Minimization 2.5.1 Golden-Section Search 2.5.2 Brent's Method 2.6 Beyond the Basics 2.6.1 Using MATLAB's Functions 2.6.2 Laguerre's Method 2.6.3 Zeros of a Nonlinear Function2.7 Chapter Wrap-Up 3 Solving Linear Systems: Direct Methods 953.1 Gaussian Elimination 3.1.1 Basic Method3.1.2 Row Pivoting .3.2 Gauss-Jordan 3.2.1 Inverse of a Matrix3.3 Tridiagonal Systems3.4 Further Topics 3.4.1 MATLAB's Methods 3.4.2 Condition of a Matrix3.4.3 Iterative Refinement 3.5 Chapter Wrap-Up 4 LU and QR Factorization 1354.1 LU Factorization 4.1.1 Using Gaussian Elimination 4.1.2 Direct LU Factorization 4.1.3 Applications 4.2 Matrix Transformations 4.2.1 Householder Transformation4.2.2 Givens Rotations 4.3 QR Factorization 4.3.1 Using Householder Transformations 4.3.2 Using Givens Rotations 4.4 Beyond the Basics 4.4.1 LU Factorization with Implicit Row Pivoting 4.4.2 Efficient Conversion to Hessenberg Form 4.4.3 Using MATLAB's Functions 4.5 Chapter Wrap-Up 5 Eigenvalues and Eigenvectors 1795.1 Power Method5.1.1 Basic Power Method 5.1.2 Rayleigh Quotient 5.1.3 Shifted Power Method 5.1.4 Accelerating Convergence 5.2 Inverse Power Method5.2.1 General Inverse Power Method5.2.2 Convergence 5.3 QR Method 5.3.1 Basic QR Method 5.3.2 Better QR Method 5.3.3 Finding Eigenvectors 5.3.4 Accelerating Convergence 5.4 Further Topics5.4.1 Singular Value Decomposition5.4.2 MATLAB's Methods5.5 Chapter Wrap-Up 6 Solving Linear Systems: Iterative Methods 2136.1 Jacobi Method 6.2 Gauss-Seidel Method6.3 Successive Over-Relaxation6.4 Beyond the Basics6.4.1 MATLAB's Built-In Functions 6.4.2 Conjugate Gradient Methods 6.4.3 GMRES6.4.4 Simplex Method 6.5 Chapter Wrap-Up 7 Nonlinear Functions of Several Variables 2517.1 Nonlinear Systems 7.1.1 Newton's Method 7.1.2 Secant Methods 7.1.3 Fixed-Point Iteration 7.2 Minimization7.2.1 Descent Methods 7.2.2 Quasi-Newton Methods7.3 Further Topics 7.3.1 Levenberg-Marquardt Method 7.3.2 Nelder-Mead Simplex Search 7.4 Chapter Wrap-Up 8 Interpolation 2758.1 Polynomial Interpolation 8.1.1 Lagrange Form 8.1.2 Newton Form 8.1.3 Difficulties 8.2 Hermite Interpolation 8.3 Piecewise Polynomial Interpolation 8.3.1 Piecewise Linear Interpolation8.3.2 Piecewise Quadratic Interpolation 8.3.3 Piecewise Cubic Hermite Interpolation8.3.4 Cubic Spline Interpolation 8.4 Beyond the Basics8.4.1 Rational-Function Interpolation 8.4.2 Using MATLAB's Functions 8.5 Chapter Wrap-Up 9 Approximation 3339.1 Least-Squares Approximation9.1.1 Approximation by a Straight Line 9.1.2 Approximation by a Parabola 9.1.3 General Least-Squares Approximation9.1.4 Approximation for Other Functional Forms9.2 Continuous Least-Squares Approximation 9.2.1 Approximation Using Powers of x9.2.2 Orthogonal Polynomials 9.2.3 Legendre Polynomials 9.2.4 Chebyshev Polynomials 9.3 Function Approximation at a Point 9.3.1 Pad'e Approximation 9.3.2 Taylor Approximation 9.4 Further Topics 9.4.1 Bezier Curves 9.4.2 Using MATLAB's Functions 9.5 Chapter Wrap-Up 10 Fourier Methods 37310.1 Fourier Approximation and Interpolation 10.1.1 Derivation 10.1.2 Data on Other Intervals 10.2 Radix-2 Fourier Transforms10.2.1 Discrete Fourier Transform 10.2.2 Fast Fourier Transform10.2.3 Matrix Form of FFT 10.2.4 Algebraic Form of FFT 10.3 Mixed-Radix FFT10.4 Using MATLAB's Functions 10.5 Chapter Wrap-Up 11 Numerical Differentiation and Integration 40511.1 Differentiation11.1.1 First Derivatives 11.1.2 Higher Derivatives 11.1.3 Partial Derivatives 11.1.4 Richardson Extrapolation 11.2 Numerical Integration 11.2.1 Trapezoid Rule 11.2.2 Simpson's Rule11.2.3 Newton-Cotes Open Formulas 11.2.4 Extrapolation Methods 11.3 Quadrature11.3.1 Gaussian Quadrature 11.3.2 Other Gauss-Type Quadratures 11.4 MATLAB's Methods 11.4.1 Differentiation11.4.2 Integration11.5 Chapter Wrap-Up 12 Ordinary Differential Equations: Fundamentals 44512.1 Euler's Method 12.1.1 Geometric Introduction 12.1.2 Approximating the Derivative 12.1.3 Approximating the Integral12.1.4 Using Taylor Series 12.2 Runge-Kutta Methods12.2.1 Second-Order Runge-Kutta Methods 12.2.2 Third-Order Runge-Kutta Methods12.2.3 Classic Runge-Kutta Method 12.2.4 Fourth-Order Runge-Kutta Methods 12.2.5 Fifth-Order Runge-Kutta Methods 12.2.6 Runge-Kutta-Fehlberg Methods12.3 Multistep Methods12.3.1 Adams-Bashforth Methods 12.3.2 Adams-Moulton Methods 12.3.3 Adams Predictor-Corrector Methods 12.3.4 Other Predictor-Corrector Methods12.4 Further Topics 12.4.1 MATLAB's Methods 12.4.2 Consistency and Convergence12.5 Chapter Wrap-Up 13 ODE: Systems, Stiffness, Stability 49913.1 Systems 13.1.1 Systems of Two ODE 13.1.2 Euler's Method for Systems 13.1.3 Runge-Kutta Methods for Systems 13.1.4 Multistep Methods for Systems 13.1.5 Second-Order ODE13.2 Stiff ODE13.2.1 BDF Methods13.2.2 Implicit Runge-Kutta Methods 13.3 Stability 13.3.1 A-Stable and Stiffly Stable Methods 13.3.2 Stability in the Limit 13.4 Further Topics13.4.1 MATLAB's Methods for Stiff ODE 13.4.2 Extrapolation Methods13.4.3 Rosenbrock Methods 13.4.4 Multivalue Methods 13.5 Chapter Wrap-Up 14 ODE: Boundary-Value Problems 56114.1 Shooting Method 14.1.1 Linear ODE 14.1.2 Nonlinear ODE 14.2 Finite-Difference Method14.2.1 Linear ODE14.2.2 Nonlinear ODE14.3 Function Space Methods 14.3.1 Collocation 14.3.2 Rayleigh-Ritz 14.4 Chapter Wrap-Up 15 Partial Differential Equations 59315.1 Heat Equation: Parabolic PDE15.1.1 Explicit Method 15.1.2 Implicit Method 15.1.3 Crank-Nicolson Method 15.1.4 Insulated Boundary15.2 Wave Equation: Hyperbolic PDE 15.2.1 Explicit Method 15.2.2 Implicit Method 15.3 Poisson Equation: Elliptic PDE 15.4 Finite-Element Method for Elliptic PDE 15.4.1 Defining the Subregions 15.4.2 Defining the Basis Functions 15.4.3 Computing the Coefficients 15.4.4 Using MATLAB 15.5 Chapter Wrap-Up Bibliography 643 Answers 653 Index 667