Customer Reviews

Calculus of Variations (Dover Books on Mathematics)

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This is the ultimate applications of variations book. The book develops the variational calculus in a pretty succinct manner and then surveys areas of application such as vibrating membranes, optics, hamiltonian mechanics, elasticity theory, quantum mechanics and electrostatics. The book has a pretty reasonable amount of problems which tend to be fairly soluble and
have the feel of an engineer's book rather than a mathematicians text. Weinstock was a Stanford math professor,so the book is

fairly rigorous but the emphasis is not on proofs. Many books on this subject require an advanced knowledge of analysis including such things as the Lebesgue integral etcetera. This is not required here this is a book that a physicist or engineer will be entirely comfortable with. There are other books that introduce the fundamentals in a shorter space Gelfand and Fomin
being my favorite, but this book covers the basics from a pretty practical perspective and includes more applications than any other calculus of variations book I know of.

Contary to the previous reviewer I generally do not care much if presentation is rigorous or not. It is much more important that the book can be understood easily, contains a lot of thoroughly selected examples which illustrate general principles. In fact, the book is written in a way allowing one to understand what is the most essential in the subject even if all proofs were omitted. Such a feature is a fingerprint of a classic.

I strongly recommend it for a standard course on variational calculus.

The importance of variational calculus cannot be overstated, as it now is being applied to myriads of different areas, these going way beyond the routine applications in physics and engineering. Indeed, it has been found to be useful in economics, network engineering, financial modeling, computational radiology, and in the new field of constraint programming. This book is now a classic, and has been the standard reference and textbook for variational calculus since its first date of publication. There have been many excellent books on variational calculus that have appeared since this one first did, but they do not provide the needed intuition in learning the subject. The clarity of the author's presentation in this book is outstanding, and, most importantly, he assigns challenging exercises to test the readers understanding of the subject. When the book was first published, computers were not being used as they are today, and the current strategy in solving variational problems is usually to use some sort of numerical software packages. In addition, the use of symbolic programming languages, such as Mathematica and Maple, have made the derivations in variational calculus almost trivial, and this is a promising trend since it allows the user to concentrate more on the concepts involved in applying it. Also, very efficient numerical routines exist in Fortran, C, and C++ that are designed and optimized for variational problems.

All of the beginning material on the calculus of variations is covered in the book, and its application to Lagrangian and Hamiltonian mechanics, elasticity, quantum mechanics, and electrostatics. Isoperimetric problems are treated, the vibrating string and membrane, and the Sturm-Liouville system and its origin as an eigenvalue problem in variational calculus. In the latter, the reader can see the origing of some of special function solutions, such as the Bessel functions and Laguerre polynomials. The reading of this book will amply prepare the reader for applying it to problems in quantum field theory, economics, radiology, financial engineering, logistics, optimization theory, computational geometry, control theory, and the theory of evolutionary strategies. In addition, the book will allow the reader to move on to more advanced areas of mathematics, such as the theory of minimal surfaces, Morse theory, and geometric measure theory.

When I firstly see this book, I don't take it seriously for its length. But after I read it, I find it's an appropriate textbook for its brevity,rigor in mathematics,and a lot of examples helping you to illustrate its application. I think the most valuable point of this book is the author's rigor in mathematics,which are often neglected by most physicists.Secondly is its master use of deduction. I recommend it heartedly.

What a nice book. Mathematically rigorous, but not in a way that loses sight of the beauty of the subject and its relevance to applications. Love the final section on quantum mechanics. They avoid the delta notation completely and I can understand why - many books that do use it define it incorrectly (Goldstein, Synge and Griffith - for a correct treatment, see Gelfand and Fomin).

The book is very good