This book is intended for a first course, at the senior or beginning
graduate level, in the calculus of variations. It will also be of use to
those interested in self-study.
There are already many excellent books on this topic. I cite a
number of these texts throughout this book. I have added another
book, this book, because I wanted a text that is especially well suited
to the Amath 507 class that I teach at the University of Washington.
My Amath 507 students are typically applied mathematicians,
physicists, and engineers. I have thus included numerous examples
from fields such as mechanics and optics; I have also included many
examples with immediate geometric appeal. Because of my students’
strong interest in applications, I have also introduced constraints ear-
lier than usual.
My students also enjoy learning the history of science. So I have
resisted the temptation of immediately jumping to the most modern
results. I instead follow the historical development of the calculus
of variations. The calculus of variations has an especially rich and
interesting history and a historical approach works exceptionally well
for this subject.
Finally, I teach on a quarter system. So I have taken the oppor-
tunity of writing this book to collect and organize my thoughts on
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