Fundamentals and Linear Algebra for the Chemical Engineer – Solving Numerical Problems SOLVING NUMERICAL PROBLEMS

Die ideale Kombination: eine vollständige und wissenschaftlich exakte Beschreibung numerischer Algorithmen, die wirklich funktionieren, plus eine Gebrauchsanweisung für die praktische Umsetzung in der Technik und angewandten Mathematik.

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.

INTRODUCTION Notation - Why C++? - BzzMath Library Style Basic Requirements for Using BzzMath Library Topics of Volume I - Topics of Companion Volumes BASIC CONCEPTS Modeling Physical Phenomena What is an Algorithm? Representatino of Real Numbers Elementary Operations Error Sources Error Analysis Local Error and Propagation Well-posed Problems Well-conditioned Formulation Algorithm Stability Algorithm Selection Questions - Excercises - References UTILITIES IN BZZMATH LIBRARY Integer Algebra Complex Numbers Questions - Excercises - References LINEAR ALGEBRA Vectors Dense Matrices Diagonal Matrices Band Matrices Left Matrices Right Matrices Staircase Matrices Sparse Matrices Block Matrices Vectors of Vectors Questions - Excercises - References SQUARE LINEAR SYSTEMS Conditioning of a Linear System Matrix Balancing Gaussian Transformation Classical Gaussian Factorization Alternative Methods for Gaussian Factorization Questions - Excercises - References TAILORED LINEAR SYSTEMS Matrices That Do Not Require Any Factorization Symmetric Matrices Sparse Matrices Symmetric Sparse Matrices Band Matrices Staircase Matrices Partially Structured Matrices Iterative Methods Questions - Excercises - References OVERDIMENSIONED LINEAR SYSTEMS Orthogonal Matrices Orthogonal Transformation QR Factorization SVD Factorization Questions - Excercises - References UNDERDIMENSIONED LINEAR SYSTEMS LQ Factorization Questions - Excercises - References EIGENVALUES AND EIGENVECTORS FOR SYMMETRIC MATRICES Eigenvalues of Symmetric Matrices Power Method Jacobi Method QR Algorithm Eigenvalues of Rank-2 Matrices Questions - Excercises - References ITERATIVE PROCESSES Convergence of an Iterative Algorithm Convergence Speed Convergence Accelerators Extrapolation Questions - Excercises - References USER-PROGRAM INTERFACE Procedural Type - Object-oriented Type APPENDICES Graphical Tools - Entertainments - How to Learn Learning