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Fundamentals and Linear Algebra for the Chemical Engineer

ISBN: 978-3-527-32552-8
375 pages
April 2010
Fundamentals and Linear Algebra for the Chemical Engineer (3527325522) cover image
A practical engineer's companion to using numerical methods for the solution of complex mathematical problems. It thus enables readers to use and implement standard numerical tools in their work, explaining the theory behind the various functions and problem solvers, while showcasing applications in diverse scientific and engineering fields.
The material is based on several tried-and-tested courses for scientists and engineers taught by the authors, and all the exercises and problems are classroom-tested.
The required software is freeware developed and maintained by the authors, included on the accompanying CD-ROM, together with an installation tutorial, all the examples and sample codes described in the book, as well as a host of additional examples.
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Preface
BASIC CONCEPTS
Introduction
Modeling Physical Phenomena
Number Representation on the Computer
Elementary Operations
Error Sources
Error Propagation
Decision-Making for an Optimal Program
Selection of Programming Languages: Why C++?

SOME UTILITIES IN THE BzzMATH LIBRARY
Introduction
Messages and Printing
Save and Load
Integer Algebra
BzzVevtorIntArray and BzzVectorArray
BzzMatrixCoefficientsExistence
BzzMatrixExistence
BzzSymmetricMatrixCoefficientsExistence
Complex Numbers
Miscellaneous Utilities
BzzPlot.exe and BzzPlotSparse.exe

LINEAR ALGEBRA
Introduction
Classes for Linear Algebra
BzzVector Class
BzzMatrix Class
Vector and Matrix Norms
Structured Matrices
Sparse Unstructured Matrices
Symmetric Matrices
Linear Algebra Operations

SQUARE LINEAR SYSTEMS
Introduction
Gauss Elimination
Gauss Transformation
Classical Gauss Factorization
Alternative Methods
Conditioning of Linear Systems
Best Pivot Selection
Solution Features
Class for Linear System Solution
Condition Number Computation
Determinant Evaluation
Inverse Matrix
Sparse Matrices
Classes for Linear System Solution with Sparse Unstructured Matrices

STRUCTURED LINEAR SYSTEMS
Introduction
Symmetric Matrices
Symmetric Sparse Matrices
Band Matrices
Diagonal Block Matrices
Iterative Methods
Systems Generated by Special Physical Problems

OVERDIMENSIONED LINEAR SYSTEMS
Introduction
Orthogonal Matrices
Problem Conditioning
Method of Least Squares
Orthogonal Transformation
QR Factorization
Classes for QRT Factorization
SVC Factorization
Class for SVD Factorization
Advantages of SVD Factorization

UNDERDIMENSIONED LINEAR SYSTEMS
Introduction
LQ Factorization
Classes for LQ Factorization
Null Space
Minimization with Linear Constraints
Minimizing a Sum of Squares Subject to Linear Constraints
Special Problems Solved by LQ Factorization

EIGENVALUES AND EIGENVECTORS FOR SYMMETRIC MATRICES
Introduction
Eigenvalues of Symmetric Matrices
Power Method
Inverse Power Method
Inverse-Translate Power Method
Jacobi Method
QR Algorithm
Eigenvalues of Rank-2 Matrices

ITERATIVE PROCESSES
Introduction
Convergence of an Iterative Algorithm
Convergence Speed
Convergence Accelerators
Extrapolation
Extrapolation Methods
Class for Numerical Derivation

APPENDIX A: Matrix Product
APPENDIX B: Entertainment
APPENDIX C: Basic Requirements for Using the BzzMath Library
APPENDIX D: Copyrights
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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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