Read more
An engineer's companion to using numerical methods for the solution of complex mathematical problems. It explains the theory behind current numerical methods and shows in a step-by-step fashion how to use them, focusing on interpolation and regression models. The methods and examples are taken from a wide range of scientific and engineering fields, including chemical engineering, electrical engineering, physics, medicine, and environmental science.The material is based on several courses for scientists and engineers taught by the authors, and all the exercises and problems are classroom-tested. The required software is provided by way of a freely accessible program library at the University of Milan that provides up-to-date software tools for all the methods described in the book.
List of contents
PrefaceINTERPOLATIONIntroductionClasses for Function InterpolationPolynomial InterpolationRoots-Product FormStandard FormLagrange MethodNewton MethodNeville AlgorithmHermite Polynomial InterpolationInterpolation with Rational FunctionsInverse InterpolationSuccessive Polynomial InterpolationTwo-Dimensional CurvesOrthogonal PolynomialsFUNDAMENTALS OF STATISTICSIntroductionFundamentalsEstimation of Expected ValueEstimation of VarianceEstimation of Standard DeviationOutlier DetectionRelevant Probability DistributionsCorrect Meaning of Statistical Tests and Confidence RegionsNonparametric StatisticsConditional ProbabilityLINEAR REGRESSIONSIntroductionLeast Sum of Squares MethodsSome CaveatClass for Linear RegressionsGeneralized Toolkit for Linear ProblemsData ModificationData DeletionPreliminary AnalysisMulticollinearityBest Model SelectionPrincipal ComponentsROBUST LINEAR REGRESSIONSIntroductionSome CaveatOutliers and Gross ErrorsStudentized ResidualsM-EstimatorsInfluential ObservationsY-Outliers, X-Outliers, and F-OutliersSecluded ObservationsRobust IndicesNormality ConditionHeteroscedasticity ConditionLINEAR REGRESSION CASE STUDIESIntroductionFerrari F1's TestBest Model FormulationOutliersBest Model SelectionPrincipal ComponentsNONLINEAR REGRESSIONSNonlinear Regression ProblemsSome CaveatParameter EvaluationBzzNonLinearRegression ClassNonalgebraic ConstraintsAlgorithms for Outlier DetectionCorrelations Among Model ParametersPreventative Model AnalysisModel DiscriminationModel Collection and Model SelectionMONLINEAR REGRESSION CASE STUDIESIntroductionOne Dependent Variable with Constant VarianceMulticubic Piecewise ModelsOne Dependent Variable and Nonconstant VarianceMore Dependent Variable and Constant VarianceMore Dependent Variable and Nonconstant VarianceModel Consisting of Ordinary Differential EquationsModel Consisting of Differential Algebraic EquationsAnalysis of Alternative ModelsIndependent Variables Subject to Experimental ErrorVariables with Missing ExperimentsOutliersIndependent Variables Subject to Experimental Error and Model with OutliersREASONABLE DESIGN OF EXPERIMENTSIntroductionPreliminary ExperimentsUsing Models to Suggest New ExperimentsNew Experiments to Improve the Parameter EstimationModel Selection: The Bayesian ApproachNew Experiments for Model DiscriminationCriterion Used in BzzNonLinearRegression Class to Generate New ExperimentsAPPENDIX A: Mixed-Language: Fortan and C++APPENDIX B: Basic Requirements for Using the BzzMath LibraryAPPENDIX C: Copyrights
About the author
Guido Buzzi-Ferraris is full professor of process systems engineering at Politecnico die Milano, Italy, where he holds two courses: "Methods and Numerical Applications in Chemical Engineering" and "Regression Models and Statistics". He works on numerical analysis, statistics, differential systems, and optimization. He has authored books of international relevance on numerical analysis, such as "Scientific C++" edited by Addison-Wesley, and over than 200 papers on international magazines. He is the inventor and the developer of BzzMath library, which is currently adopted by academies, R&D groups, and industries. He is permanent member of the "EFCE Working Party - Computer Aided Process Engineering" since 1969 and editorial advisory board of "Computers & Chemical Engineering" since 1987.
Flavio Manenti is assistant professor of process systems engineering at Politecnico di Milano, Italy. He obtained his academic degree and PhD at Politecnico di Milano, where he currently collaborates with Professor Buzzi-Ferraris. He holds courses on "Process Dynamics and Control of Industrial Processes" and "Supply Chain Optimization" and he works on numerical analysis, process control and optimization. He has also received international scientific awards, such as Memorial Burianec (Prague, CZ) and Excellence in Simulation (Lake Forest, CA, USA), for his research activities and scientific publications.
Summary
Die ideale Kombination: Numerische Algorithmen, die wirklich funktionieren, wissenschaftlich exakt erklärt, plus ein praxisgeeigneter Leitfaden für ihre Anwendung vor allem im ingenieurtechnischen Umfeld!
