Nature tries to minimize the surface area of a soap film through
the action of surface tension. The process can be understood
mathematically by using differential geometry, complex analysis, and
the calculus of variations. This book employs ingredients from each of
these subjects to tell the mathematical story of soap films.

The text is fully self-contained, bringing together a mixture of types of
mathematics along with a bit of the physics that underlies the subject. The
development is primarily from first principles, requiring no advanced
background material from either mathematics or physics.

Through the Maple® applications, the reader is given tools for
creating the shapes that are being studied. Thus, you can
“see” a fluid rising up an inclined plane, create minimal
surfaces from complex variables data, and investigate the
“true” shape of a balloon. Oprea also includes descriptions
of experiments and photographs that let you see real soap films on
wire frames.

The theory of minimal surfaces is a beautiful subject, which naturally
introduces the reader to fascinating, yet accessible, topics in mathematics.
Oprea's presentation is rich with examples, explanations, and applications. It
would make an excellent text for a senior seminar or for independent study by
upper-division mathematics or science majors.

Readership

Advanced undergraduates, graduate students, and mathematicians
interested in the mathematics of soap films.