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基本説明
Assuming some knowledge of calculus, this text offers numerous applied examples and exercises related to numerical methods. Supplementary CD-ROM contains MATLAB functions that give clear, step-by-step explanations. This edition includes a new chapter on numerical methods for linear integral equations.
Full Description
Highly recommended by CHOICE, previous editions of this popular textbook offered an accessible and practical introduction to numerical analysis. An Introduction to Numerical Methods: A MATLAB (R) Approach, Third Edition continues to present a wide range of useful and important algorithms for scientific and engineering applications. The authors use MATLAB to illustrate each numerical method, providing full details of the computer results so that the main steps are easily visualized and interpreted.New to the Third EditionA chapter on the numerical solution of integral equationsA section on nonlinear partial differential equations (PDEs) in the last chapterInclusion of MATLAB GUIs throughout the textThe book begins with simple theoretical and computational topics, including computer floating point arithmetic, errors, interval arithmetic, and the root of equations. After presenting direct and iterative methods for solving systems of linear equations, the authors discuss interpolation, spline functions, concepts of least-squares data fitting, and numerical optimization. They then focus on numerical differentiation and efficient integration techniques as well as a variety of numerical techniques for solving linear integral equations, ordinary differential equations, and boundary-value problems. The book concludes with numerical techniques for computing the eigenvalues and eigenvectors of a matrix and for solving PDEs.CD-ROM ResourceThe accompanying CD-ROM contains simple MATLAB functions that help students understand how the methods work. These functions provide a clear, step-by-step explanation of the mechanism behind the algorithm of each numerical method and guide students through the calculations necessary to understand the algorithm.Written in an easy-to-follow, simple style, this text improves students' ability to master the theoretical and practical elements of the methods. Through this book, they will be able to solve many numerical problems using MATLAB.
Contents
IntroductionAbout MATLAB and MATLAB graphical user interface (GUI)An introduction to MATLABTaylor seriesNumber System and ErrorsFloating-point arithmeticRound-off errorsTruncation errorInterval arithmeticRoots of EquationsThe bisection methodThe method of false positionFixed-point iterationThe secant methodNewton's methodConvergence of the Newton and Secant methodsMultiple roots and the modified Newton methodNewton's method for nonlinear systemsApplied problemsSystem of Linear EquationsMatrices and matrix operationsNaive Gaussian eliminationGaussian elimination with scaled partial pivotingLu decompositionIterative methodsApplied problemsInterpolationPolynomial interpolation theoryNewton's divided-difference interpolating polynomialThe error of the interpolating polynomialLagrange interpolating polynomial Applied problemsInterpolation with Spline FunctionsPiecewise linear interpolationQuadratic splineNatural cubic splinesApplied problemsThe Method of Least SquaresLinear least squaresLeast-squares polynomialNonlinear least squaresTrigonometric least-squares polynomial Applied problemsNumerical OptimizationAnalysis of single-variable functionsLine search methodsMinimization using derivativesApplied problemsNumerical DifferentiationNumerical differentiationRichardson's formulaApplied problemsNumerical IntegrationTrapezoidal ruleSimpson's ruleRomberg algorithmGaussian quadratureApplied problemsNumerical Methods for Linear Integral EquationsIntroductionQuadrature rulesThe successive approximation methodSchmidt's methodVolterra-type integral equationsApplied problemsNumerical Methods for Differential EquationsEuler's MethodError AnalysisHigher-order Taylor series methodsRunge-Kutta methodsAdams-Bashforth methodsPredictor-corrector methodsAdams-Moulton methodsNumerical stabilityHigher-order equations and systems of differential equationsImplicit methods and stiff systemsPhase plane analysis: chaotic differential equationsApplied problemsBoundary-Value ProblemsFinite-difference methodsShooting methodsApplied problemsEigenvalues and EigenvectorsBasic theory The power methodThe quadratic methodEigenvalues for boundary-value problemsBifurcations in differential equationsApplied problemsPartial Differential EquationsParabolic equationsHyperbolic equationsElliptic equationsNonlinear partial differential equationsIntroduction to finite-element methodApplied problemsBibliography and ReferencesAppendix A: Calculus ReviewAppendix B: MATLAB Built-in FunctionsAppendix C: Text MATLAB FunctionsAppendix D: MATLAB GUIAnswers to Selected Exercises Index
