Interpolation and Regression Models for the Chemical Engineer

  • ID: 2183317
  • Book
  • 442 Pages
  • John Wiley and Sons Ltd
1 of 4
An engineer′s companion for using numerical methods for the solution of complex mathematical problems. It explains the theory behind current numerical methods and shows how to use them in a step–by–step fashion, focusing on interpolation and regression models.

The methods and examples are taken from a wide range of scientific and engineering fields, including chemical and 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 software needed is available 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.
Note: Product cover images may vary from those shown
2 of 4
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
Note: Product cover images may vary from those shown
3 of 4

Loading
LOADING...

4 of 4
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.

Note: Product cover images may vary from those shown
5 of 4
Note: Product cover images may vary from those shown
Adroll
adroll