The Calculus of Variations [Paperback]

Suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering, this introduction to the calculus of variations focuses on variational problems involving one independent variable. It also discusses more advanced topics such as the inverse problem, eigenvalue problems, and Noethers theorem. The text includes numerous examples along with problems to help students consolidate the material.

Thecalculusofvariationshasalonghistoryofinteractionwithotherbranches of mathematics such as geometry and di?erential equations, and with physics, particularly mechanics. More recently, the calculus of variations has found applicationsinother?eldssuchaseconomicsandelectricalengineering. Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations. This book is an introduction to the calculus of variations for mathema- cians and scientists. The reader interested primarily in mathematics will ?nd results of interest in geometry and di?erential equations. I have paused at times to develop the proofs of some of these results, and discuss brie?y v- ious topics not normally found in an introductory book on this subject such as the existence and uniqueness of solutions to boundary-value problems, the inverse problem, and Morse theory. I have made passive use of functional analysis (in particular normed vector spaces) to place certain results in c- text and reassure the mathematician that a suitable framework is available for a more rigorous study. For the reader interested mainly in techniques and applications of the calculus of variations, I leavened the book with num- ous examples mostly from physics. In addition, topics such as Hamiltons Principle, eigenvalue approximations, conservation laws, and nonholonomic constraints in mechanics are discussed. More importantly, the book is written on two levels. The technical details for many of the results can be skipped on the initiallS