Interpolation and Regression Models for the Chemical Engineer: Solving Numerical Problems

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.

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

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.