Overview

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.

Full Product Details

Author:   Guido Buzzi-Ferraris (Politecnico di Milano, Italy) ,  Flavio Manenti (Politecnico di Milano, Italy)
Publisher:   Wiley-VCH Verlag GmbH
Imprint:   Blackwell Verlag GmbH
Dimensions:   Width: 17.80cm , Height: 2.80cm , Length: 24.60cm
Weight:   0.962kg
ISBN:  

9783527326525

ISBN 10:   3527326529
Pages:   442
Publication Date:   24 March 2010
Audience:   College/higher education ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   Out of stock  

Table of Contents

Preface INTERPOLATION Introduction Classes for Function Interpolation Polynomial Interpolation Roots-Product Form Standard Form Lagrange Method Newton Method Neville Algorithm Hermite Polynomial Interpolation Interpolation with Rational Functions Inverse Interpolation Successive Polynomial Interpolation Two-Dimensional Curves Orthogonal Polynomials FUNDAMENTALS OF STATISTICS Introduction Fundamentals Estimation of Expected Value Estimation of Variance Estimation of Standard Deviation Outlier Detection Relevant Probability Distributions Correct Meaning of Statistical Tests and Confidence Regions Nonparametric Statistics Conditional Probability LINEAR REGRESSIONS Introduction Least Sum of Squares Methods Some Caveat Class for Linear Regressions Generalized Toolkit for Linear Problems Data Modification Data Deletion Preliminary Analysis Multicollinearity Best Model Selection Principal Components ROBUST LINEAR REGRESSIONS Introduction Some Caveat Outliers and Gross Errors Studentized Residuals M-Estimators Influential Observations Y-Outliers, X-Outliers, and F-Outliers Secluded Observations Robust Indices Normality Condition Heteroscedasticity Condition LINEAR REGRESSION CASE STUDIES Introduction Ferrari F1's Test Best Model Formulation Outliers Best Model Selection Principal Components NONLINEAR REGRESSIONS Nonlinear Regression Problems Some Caveat Parameter Evaluation BzzNonLinearRegression Class Nonalgebraic Constraints Algorithms for Outlier Detection Correlations Among Model Parameters Preventative Model Analysis Model Discrimination Model Collection and Model Selection MONLINEAR REGRESSION CASE STUDIES Introduction One Dependent Variable with Constant Variance Multicubic Piecewise Models One Dependent Variable and Nonconstant Variance More Dependent Variable and Constant Variance More Dependent Variable and Nonconstant Variance Model Consisting of Ordinary Differential Equations Model Consisting of Differential Algebraic Equations Analysis of Alternative Models Independent Variables Subject to Experimental Error Variables with Missing Experiments Outliers Independent Variables Subject to Experimental Error and Model with Outliers REASONABLE DESIGN OF EXPERIMENTS Introduction Preliminary Experiments Using Models to Suggest New Experiments New Experiments to Improve the Parameter Estimation Model Selection: The Bayesian Approach New Experiments for Model Discrimination Criterion Used in BzzNonLinearRegression Class to Generate New Experiments APPENDIX A: Mixed-Language: Fortan and C++ APPENDIX B: Basic Requirements for Using the BzzMath Library APPENDIX C: Copyrights

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Author Information

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.

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