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Brunt gives us a nice historical introduction to the calculus of variations. "Bruce van Brunt shows his love of the subject in his new book The Calculus of Variations …. Kunzinger, Monatshefte für Mathematik, Vol. … Due to its concrete and well-organized approach, the book constitutes a valuable addition to the text book literature on the calculus of variations." (M. … The emphasis is on well-chosen examples used to obtain the necessary heuristics for developing the theoretical background. "This text provides a friendly and … elementary introduction to the calculus of variations.

" (Matthew Roughan, The Australian Mathematical Society Gazette, Vol.

The book really brought home to me the elegance of this subject …. Overall I enjoyed this book, and would unreservedly recommend it …. From my perspective, the book was pitched at a good level for the students I was teaching …. … Accordingly, I chose to use this book as my primary reference for presenting the course …. "The author describes this book as suitable for a one semester course for advance undergraduate students in math, physics or engineering. " (Nick Lord, The Mathematical Gazette, Vol. There is sufficient meat, both in the range of examples treated and in the development of the underlying mathematics … that most of its intended audience will just be grateful …. can be used in a variety of undergraduate and beginning postgraduate courses. Brunt writes in a lucid, engaging style …. I enjoyed reading The calculus of variations. As such, it is intended to be a non-intimidating, introductory text …. "The calculus of variations is one of the latest books in Springer’s Universitext series. Stachó, Acta Scientiarum Mathematicarum, Vol. It can also be appreciated that the author tries to present the results showing motivation and heuristical ideas for each crucial theorem." (L. According to my classroom experience with undergraduate physicists, the presentation of the examples in the book may be very helpful …. It is written with a deep pedagogical attention …. "I find this book a very useful supplementary reading for undergraduate students and a good teaching aid for lecturers of topics involving traditional variational calculus (as e. The student can thus learn the main results in each chapter and return as needed to the proofs for a deeper understanding. The technical details for many of the results can be skipped on the initial reading. More importantly, the book is written on two levels. In addition, topics such as Hamilton’s Principle, eigenvalue approximations, conservation laws, and nonholonomic constraints in mechanics are discussed. For the reader interested mainly in techniques and applications of the calculus of variations, I leavened the book with numerous examples mostly from physics. I have made “passive use” of functional analysis (in particular normed vector spaces) to place certain results in context and reassure the mathematician that a suitable framework is available for a more rigorous study. I have paused at times to develop the proofs of some of these results, and discuss briefly various 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. The reader interested primarily in mathematics will find results of interest in geometry and differential equations. This book is an introduction to the calculus of variations for mathematicians and scientists.

Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations.

More recently, the calculus of variations has found applications in other fields such as economics and electrical engineering. The calculus of variations has a long history of interaction with other branches of mathematics such as geometry and differential equations, and with physics, particularly mechanics.