cal soap films) and the uses of minimal surfaces in science, engineering
and architecture, while [Mor88] presents an introduction to geomet-
ric measure theory (the modern approach to minimal surfaces) which
every budding geometer should read. For a straightforward discussion
of surface tension and its effects, [Ise92] can't be beat.
In the past, minimal surfaces have been considered in differen-
tial geometry books as an add-on ([Gra93], [Opr97]) and in other
books at perhaps too high a level for undergraduates. Also, the basics
of surface tension have not been discussed in these books, but left to
higher-level texts ([Fin86]) or books tending more toward the physics
side of things ([Ise92]). So a major goal of this book is simply to make
available a self-contained text where undergraduates can see a mix-
ture of the different types of mathematics which pertain to minimal
surfaces together with a bit of the science behind the subject. Most
undergraduates only see the standard applications of mathematics to
physical systems, where answers are typically only analytic. Here
they can see another way that mathematics applies to science the
determination of optimal shape.
Since this book concentrates on shape, it would be a shame not
to present the reader with ways of creating shapes. With this in
mind, almost 40% of the book is devoted to exploring various notions
using the software package Maple. So, in the last third of the book,
the reader will 'see' fluids rising up inclined planes, create minimal
surfaces from complex variable data and investigate the 'true' shape
of a balloon. In fact, rather than reading the book in order, the
reader is recommended to jump back and forth from the mathematical
exposition to the relevant Maple work. It really pays nowdays for
undergraduates to learn a package such as Maple or Mathematica, so
the Maple work given is usually discussed at length. There is much
Previous Page Next Page