# Numerical Methods for Chemical Engineers with MATLAB Applications

## Alkis Constantinides; Navid Mostoufi

Master numerical methods using MATLAB, today's leading software for problem solving.

This complete guide to numerical methods in chemical engineering is the first to take full advantage of MATLAB's powerful calculation environment. Every chapter contains several examples using general MATLAB functions that implement the method and can also be applied to many other problems in the same category.

The authors begin by introducing the solution of nonlinear equations using several standard approaches, including methods of successive substitution and linear interpolation; the Wegstein method, the Newton-Raphson method; the Eigenvalue method; and synthetic division algorithms. With these fundamentals in hand, they move on to simultaneous linear algebraic equations, covering matrix and vector operations; Cramer's rule; Gauss methods; the Jacobi method; and the characteristic-value problem. Additional coverage includes:

Finite difference methods, and interpolation of equally and unequally spaced points

Numerical differentiation and integration, including differentiation by backward, forward, and central finite differences; Newton-Cotes formulas; and the Gauss Quadrature

Two detailed chapters on ordinary and partial differential equations

Linear and nonlinear regression analyses, including least squares, estimated vector of parameters, method of steepest descent, Gauss-Newton method, Marquardt Method, Newton Method, and multiple nonlinear regression

The numerical methods covered here represent virtually all of those commonly used by practicing chemical engineers. The focus on MATLAB enables readers to accomplish more, with less complexity, than was possible with traditional FORTRAN. For those unfamiliar with MATLAB, a brief introduction is provided as an Appendix.

Over 60+ MATLAB examples, methods, and function scripts are covered, and all of them are included on the book's CD

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From the Inside Flap:

Preface
This book emphasizes the derivation of a variety of numerical methods and their application to the solution of engineering problems, with special attention to problems in the chemical engineering field. These algorithms encompass linear and nonlinear algebraic equations, eigenvalue problems, finite difference methods, interpolation, differentiation and integration, ordinary differential equations, boundary-value problems, partial differential equations, and linear and nonlinear regression analysis.

MATLAB 2 is adopted as the calculation environment throughout the book. MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment. MATLAB is distinguished by its ability to perform all the calculations in matrix form, its large library of built-in functions, its strong structural language, and its rich graphical visualization tools. In addition, MATLAB is available on all three operating platforms: WINDOWS, Macintosh, and UNIX. The reader is expected to have a basic knowledge of using MATLAB. However, for those who are not familiar with MATLAB, it is recommended that they cover the subjects discussed in Appendix A: Introduction to MATLAB prior to studying the numerical methods. Several worked examples are given in each chapter to demonstrate the numerical techniques. Most of these examples require computer programs for their solution. These programs were written in the MATLAB language and are compatible with MATLAB 5.0 or higher. In all the examples, we tried to present a general MATLAB function that implements the method and that may be applied to the solution of other problems that fall in the same category of application as the worked example. The general algorithm for these programs is illustrated in the section entitled, "General Algorithm for the Software Developed in this Book." All the programs that appear in the text are included on the CD-ROM that accompanies this book. There are three versions of these programs on the CD-ROM, one for each of the major operating systems in which MATLAB exists: WINDOWS, Macintosh, and UNIX. Installation procedures, a complete list, and brief descriptions of all the programs are given in the section entitled "Programs on the CD-ROM" that immediately follows this Preface. In addition, the programs are described in detail in the text in order to provide the reader with a thorough background and understanding of how MATLAB is used to implement the numerical methods. It is important to mention that the main purpose of this book is to teach the student numerical methods and problem solving, rather than to be a MATLAB manual. In order to assure that the student develops a thorough understanding of the numerical methods and their implementation, new MATLAB functions have been written to demonstrate each of the numerical methods covered in this text. Admittedly, MATLAB already has its own built-in functions for some of the methods introduced in this book. We mention and discuss the built-in functions, whenever they exist. The material in this book has been used in undergraduate and graduate courses in the Department of Chemical and Biochemical Engineering at Rutgers University.

Basic and advanced numerical methods are covered in each chapter. Whenever feasible, the more advanced techniques are covered in the last few section s of each chapter. A one-semester graduate level course in applied numerical methods would cover all the material in this book. An undergraduate course (junior or senior level) would cover the more basic methods in each chapter. To facilitate the professor teaching the course, we have marked with an asterisk (*) in the Table of Contents those sections that may be omitted in an undergraduate course. Of course, this choice is left to the discretion of the professor.

Prentice Hall and the authors would like to thank the reviewers of this book for their constructive comments and suggestions. NM is grateful to Professor Jamal Chaouki of Ecole Polytechnique de Montréal for his support and understanding.

Alkis Constantinides Navid Mostoufi

Programs on the CD-ROM

Brief Description
The programs contained on the CD-ROM that accompanies this book have been written in the MATLAB 5.0 language and will execute in the MATLAB command environment in all three operating systems (WINDOWS, Macintosh, and UNIX). There are 21 examples, 29 methods, and 13 other function scripts on this CD-ROM. A list of the programs is given later in this section. Complete discussions of all programs are given in the corresponding chapters of the text. MATLAB is a high-performance language for technical computing. It integrates computation,visualization, and programming in an easy-to-use environment. It is assumed that the user has access to MATLAB. If not, MATLAB may be purchased from:
The MathWorks, Inc.
24 Prime Park Way
Natick, MA 07160-1500
Tel: 508-647-7000
Fax: 508-647-7001
E-mail: info@mathworks
mathworks
The Student Edition of MATLAB may be obtained from:
Prentice Hall PTR, Inc.
One Lake Street
Upper Saddle River, NJ 07458
prenhall
An introduction to MATLAB fundamentals is given in Appendix A of this book.

Program Installation for WINDOWS.

To start the installation, do the following:
Insert the CD-ROM in your CD-ROM drive (usually d: or e:) Choose Run from the WINDOWS Start menu, type d: (or e: ) and click OK.

ALKIS CONSTANTINIDES is a member of the faculty in the Department of Chemical and Biochemical Engineering at Rutgers, The State University of New Jersey.

NAVID MOSTOUFI is a member of the faculty in the Department of Chemical Engineering, University of Tehran, Iran.

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