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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 Edition
A chapter on the numerical solution of integral equationsA section on nonlinear partial differential equations (PDEs) in the last chapterInclusion of MATLAB GUIs throughout the text
The 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.
Abdelwahab Kharab is an associate professor in the College of Arts and Sciences at Abu Dhabi University. His research interests include numerical analysis and simulation for the numerical solution of partial differential equations that arise in science and engineering. Ronald B. Guenther is an Emeritus Professor in the Department of Mathematics at Oregon State University. His research interests include mathematically modeling deterministic systems and the ordinary and partial differential equations that arise from these models.
IntroductionAbout MATLAB and MATLAB graphical user interface (GUI)An introduction to MATLABTaylor series Number System and ErrorsFloating-point arithmeticRound-off errorsTruncation errorInterval arithmetic Roots 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 problems System of Linear EquationsMatrices and matrix operationsNaive Gaussian eliminationGaussian elimination with scaled partial pivotingLu decompositionIterative methodsApplied problems InterpolationPolynomial interpolation theoryNewton's divided-difference interpolating polynomialThe error of the interpolating polynomialLagrange interpolating polynomial Applied problems Interpolation with Spline FunctionsPiecewise linear interpolationQuadratic splineNatural cubic splinesApplied problems The Method of Least SquaresLinear least squaresLeast-squares polynomialNonlinear least squaresTrigonometric least-squares polynomial Applied problems Numerical OptimizationAnalysis of single-variable functionsLine search methodsMinimization using derivativesApplied problems Numerical DifferentiationNumerical differentiationRichardson's formulaApplied problems Numerical IntegrationTrapezoidal ruleSimpson's ruleRomberg algorithmGaussian quadratureApplied problems Numerical Methods for Linear Integral EquationsIntroductionQuadrature rulesThe successive approximation methodSchmidt's methodVolterra-type integral equationsApplied problems Numerical 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 problems Boundary-Value ProblemsFinite-difference methodsShooting methodsApplied problems Eigenvalues and EigenvectorsBasic theory The power methodThe quadratic methodEigenvalues for boundary-value problemsBifurcations in differential equationsApplied problems Partial Differential EquationsParabolic equationsHyperbolic equationsElliptic equationsNonlinear partial differential equationsIntroduction to finite-element methodApplied problems Bibliography and References Appendix A: Calculus ReviewAppendix B: MATLAB Built-in FunctionsAppendix C: Text MATLAB FunctionsAppendix D: MATLAB GUI Answers to Selected Exercises Index
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- ID: 9781439868997
3rd New edition
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