** A
brief description of the text**

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 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, we have provided a short introduction to MATLAB in the appendix of
the book (Appendix A: Introduction to MATLAB).

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 sections 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.