Preface
What is mathematics of physics and engineering? An immediate answer
would be "all mathematics that is used in physics and engineering", which is
pretty much ... all the mathematics there is. While it is nearly impossible
to present all mathematics in a single book, many books on the subject
seem to try this.
On the other hand, a semester-long course in mathematics of physics
and engineering is a more well-defined notion, and is present in most univer-
sities. Usually, this course is designed for advanced undergraduate students
who are majoring in physics or engineering, and who are already familiar
with multi-variable calculus and ordinary differential equations. The basic
topics in such a course include introduction to Fourier analysis and partial
differential equations, as well as a review of vector analysis and selected top-
ics from complex analysis and ordinary differential equations. It is therefore
useful to have a book that covers these topics — and nothing else. Besides
the purely practical benefits, related to the reduction of the physical di-
mensions of the volume the students must carry around, the reduction of
the number of topics covered has other advantages over the existing lengthy
texts on engineering mathematics.
One major advantage is the opportunity to explore the connection be-
tween mathematical models and their physical applications. We explore
this connection to the fullest and show how physics leads to mathematical
models and conversely, how the mathematical models lead to the discovery
of new physics. We believe that students will be stimulated by this inter-
play of physics and mathematics and will see mathematics come alive. For
example, it is interesting to establish the connection between electromag-
netism and Maxwell's equations on the one side and the integral theorems
of vector calculus on the other side. Unfortunately, Maxwell's equations
vii