Numerical Analysis for Engineers: Methods and Applications, Second Edition (Hardcover, 2)

IntroductionNumerical Analysis in EngineeringAnalytical versus Numerical AnalysisTaylor Series ExpansionApplicationsProblemsMatricesIntroductionVectorsDeterminantsRank of a MatrixApplicationsProblemsIntroduction to Numerical MethodsIntroductionAccuracy, Precision, and BiasSignificant FiguresAnalysis of Numerical ErrorsAdvantages and Disadvantages of Numerical MethodsApplicationsProblemsRoots of EquationsIntroductionEigenvalue AnalysisDirect-Search MethodBisection MethodNewton?Raphson IterationSecant MethodPolynomial ReductionSynthetic DivisionMultiple RootsSystems of Nonlinear EquationsApplicationsProblemsSimultaneous Linear EquationsIntroductionGaussian EliminationGauss?Jordan EliminationAdditional Considerations for Elimination ProceduresLU DecompositionIterative Equation-Solving MethodsUse of DeterminantsMatrix InversionApplicationsProblemsNumerical InterpolationIntroductionMethod of Undetermined CoefficientsGregory?Newton Interpolation MethodFinite-Difference InterpolationNewton’s MethodLagrange PolynomialsInterpolation Using SplinesGuidelines for Choice of Interpolation MethodMultidimensional InterpolationApplicationsProblemsDifferentiation and IntegrationNumerical DifferentiationNumerical IntegrationApplicationsProblemsDifferential EquationsIntroductionTaylor Series ExpansionEuler’s MethodModified Euler’s MethodRunge?Kutta MethodsPredictor?Corrector MethodsLeast-Squares MethodGalerkin MethodHigher Order Differential EquationsBoundary-Value ProblemsIntegral EquationsApplicationsProblemsData Description and TreatmentIntroductionClassification of DataGraphical Description of DataHistograms and Frequency DiagramsDescriptive MeasuresApplicationsProblemsCurve Fitting and Regression AnalysisIntroductionCorrelation AnalysisIntroduction to RegressionPrinciple of Least SquaresReliability of the Regression EquationCorrelation versus RegressionApplications of Bivariate Regression AnalysisMultiple Regression AnalysisRegression Analysis of Nonlinear ModelsApplicationsProblemsNumerical OptimizationIntroductionThe Response Surface AnalysisNumerical Least SquaresSteepest Descent MethodIllustrating ApplicationsApplicationsConcluding RemarksProblems