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