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Paperback An Introduction to the Calculus of Variations Book

ISBN: 0486654990

ISBN13: 9780486654997

An Introduction to the Calculus of Variations

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Book Overview

An understanding of variational methods, the source of such fundamental theorems as the principle of least action and its various generalizations, is essential to the study of mathematical physics and applied mathematics. In this highly regarded text, aimed at advanced undergraduate and graduate students in mathematics, the author develops the calculus of variations both for its own intrinsic interest and because of its wide and powerful applications to modern mathematical physics. The first two chapters deal with the first and second variation of an integral in the simplest case, illustrated by applications of the principle of least action to dynamical problems. Chapters III and IV delve into pure mathematics, exploring generalizations and isoperimetrical problems. Applied mathematics are discussed in Chapters V, VI, and VII, including studies of least action, a proof of Hamilton's principle and its use in dealing with dynamical problems in the special theory of relativity, and such methods of approximation as the Rayleigh-Ritz method, illustrated by applications to the theory of elasticity. The last three chapters examine variable end points and strong variations, including an account of Weierstrass's theory of strong variations, based upon the work of Hilbert. Ideal as a text, this volume offers an exceptionally clear presentation of the mathematics involved, with many illustrative examples, while numerous references cite additional source readings for those interested in pursuing a topic further. Students are assumed to have a knowledge of partial differentiation and differential equations.

Customer Reviews

2 customer ratings | 2 reviews

Rated 4 stars
Geared for classical mechanics

Good books on the calculus of variations are not thick on the ground, and this one is pretty good. It is organised around explicating Hamiltonian mechanics, but with mathematical rigor and clarity. Why not 5 stars then? Some proofs skip a lot of steps. There are not a lot of examples. The typesetting is from 509 years ago, with equations and so on in the text not on a separate line. There are few diagrams. If your interest...

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Rated 5 stars
Excellent Book on the Calculus of Variations

Thorough, concise, enjoyable and CHEAP book on the Calculus of variations. One of the few mathematics books that is simultaneously rigorous and entertaining. Illustrated with many examples and applications, drawn from physics and engineering. The proofs are brisk, though there is enough there to guide you on your way to complete understanding. A DEFINITE read for any mathematician or scientist!

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