Preface 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 ix
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