This is a book about mathematical modelling. It focuses on the modelling
of the preparation of materials. Materials are important, of course, in
an economic sense: the "goods" of goods-and-services are made of
materials. This provides a strong incentive to produce good materials
and to improve existing materials. Mathematical modelling can help in
this regard. Without a doubt, modelling a materials processing operation
is not strictly necessary. Materials synthesis and fabrication processes
certainly existed before the invention of mathematics and computers, and
well before the combined use of mathematics and computers. Modelling
can, however, be of assistance--if done properly--and if used properly.
The mathematical modelling described in this book is, at its root, a
rather formal, structured way of thinking about materials synthesis and
fabrication processes. It requires looking at a process as a whole. It
requires considering everything that is or might be important. It
requires translating the details of a given physical process into one or
more mathematical equations. It requires knowing how to simplify the
equations without over-simplifying them.