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Summary
Summary
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.
Author Notes
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.
Table of Contents
Introduction |
Notation - |
BzzMath Library Style |
Basic Requirements for Using the BzzMath Library |
Topics of Volume II - |
Topics of Companion Volumes |
Interpolation |
Polynomial Interpolation |
Hermit Polynomial Interpolation |
Interpolation with Rational Functions |
Comparision between Polynomial Interpolation and Interpolation with Rational Functions |
Inverse Interpolation |
Successive Polynomials Interpolation |
Orthogonla Polynomials |
Questions - |
Excercises - |
References |
Fundamentals Of Statistics |
Fundamentals |
Estimate of the Expected Value |
Estimation of Variance |
Outliers Detection |
Relevant Probability Distributions |
Correct Meaning of Statistical Tests and Confidence Regions |
Questions - |
Excercises - |
References |
Linear Regressions |
Linear Models and Method of Least Squares |
Hypotheses for Linear Regression Problems |
Outliers Detection and Robust Regression |
Homoscedasticity |
Multicollinearity |
BzzLinearRegression Toolkit |
Questions - |
Excercises - |
References |
Nonlinear Regressions |
Nonlinear Regression Problems |
Models Reformulation |
Parameters Evaluation |
Outliers Detection |
Parameters Estimation Improvements |
Model Discrimination |
Simultaneous Discrimination and Accurate Parameters Estimation |
Questions - |
Excercises - |
References |
Appendices |