I began this book while serving as the Gulf Professor of Chemical
Engineering at Carnegie Mellon University - indeed, without that sabbatical the
book could not have been written. The faculty there was very supportive of my
efforts and the University provided important library and office facilities. My
time there was too short to finish the book and it has been a slowly simmering
project ever since.
The book was written on the Macintoshв„ў computer and many of the
ideas developed while writing the book were possible because of the graphics
programs which could be used to demonstrate the results. The equations - of
which there are many - were written using the program Math Writerв„ў. This
equation writing software is so easy to use that some of the algebra was done on
the computer (substituting one equation into another, etc.). There are equations
in the book that have never been written down by hand. Also, since equation
writing was so simple, I tended to merely repeat an equation rather than refer back
to an earlier chapter for it. Thus the reader can follow the ideas more easily.
You will notice many graphs in the book; these were important in the
testing of the ideas. Oftentimes an author in the literature will present a new
method and present results from it, but there may be no comprehensive compari-
son with other methods. Thus I felt it important to try all methods on all problems,
insofar as that is possible. The graphical display helps decide which methods to
keep and which ones to discard. It is also possible to learn things graphically that
are harder to learn otherwise. For example, the von Neumann analysis of stability
can be tedious when done algebraically, so I show graphical results which present
the same information. They are not merely graphical displays of the algebraic
results, but are graphical presentations of the information contained in the
algebraic results - without generation of the algebraic results. For example, if you
want to see in what regions of the x-y plane a function f(x,y) is less than one, you
usually set f=l and solve for x(y) or y(x). However, you can also plot f(x,y) and
see where it is 1, and you can plot contours where f=l. These approaches are much
faster and are necessary when dealing with dozens of methods, as I was. To learn
the material in the book it is necessary that you exercise the computer programs
provided. I have witnessed students learning things much faster by operating the
computer program, chiefly because of its graphical output. To some extent the
graphical display helps you use the right side of your brain - and this is ideally
suited to a generation raised on TV!