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Calculus of Variations

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Based on a series of lectures given by I. M. Gelfand at Moscow State University, this book actually goes considerably beyond the material presented in the lectures. The aim is to give a treatment of the elements of the calculus of variations in a form both easily understandable and sufficiently modern. Considerable attention is devoted to physical applications of variational methods, e.g., canonical equations, variational principles of mechanics, and conservation laws.
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Calculus of Variations

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Overview

Based on a series of lectures given by I. M. Gelfand at Moscow State University, this book actually goes considerably beyond the material presented in the lectures. The aim is to give a treatment of the elements of the calculus of variations in a form both easily understandable and sufficiently modern. Considerable attention is devoted to physical applications of variational methods, e.g., canonical equations, variational principles of mechanics, and conservation laws.
The reader who merely wishes to become familiar with the most basic concepts and methods of the calculus of variations need only study the first chapter. Students wishing a more extensive treatment, however, will find the first six chapters comprise a complete university-level course in the subject, including the theory of fields and sufficient conditions for weak and strong extrema. Chapter 7 considers the application of variational methods to the study of systems with infinite degrees of freedom, and Chapter 8 deals with direct methods in the calculus of variations. The problems following each chapter were made specially for this English-language edition, and many of them comment further on corresponding parts of the text. Two appendices and suggestions for supplementary reading round out the text.
Substantially revised and corrected by the translator, this inexpensive new edition will be welcomed by advanced undergraduate and graduate students of mathematics and physics.

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Product Details

  • ISBN-13: 9780486414485
  • Publisher: Dover Publications
  • Publication date: 10/16/2000
  • Series: Dover Books on Mathematics Series
  • Pages: 240
  • Sales rank: 387,147
  • Product dimensions: 5.30 (w) x 8.40 (h) x 0.60 (d)

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Sort by: Showing all of 3 Customer Reviews
  • Anonymous

    Posted June 11, 2003

    An execellent Introductory Book in Variational Calculus

    Readable books on Calculus of Variations are hard to come by, if not non-existent. This is one of the clearest and most readable and self-contained books in the topic. I used it in a fourth year course at Simon Fraser University, BC, Canada. This is an introductory book meant for undergraduates and it is very well suited for this level. I strongly recommend that all serious students in Physics, Chemistry, engineering, and computing science, take a serious look at the book as a starting point in studying this most underated and relevant topic as a necessary mathematical foundation. Virually all fundamental laws of Physics, Chemistry, and Engineering has their origins from some form of Variational Prinicples. If anyone is interested in pursuing this topic, this should definitely the first book one should read. The student should be equipped with at least one introductory course in Real Ananlysis in order to start studying Variational Calculus. Just a practical (cook-book) style applied mathematics course in Calculus and Differential Equations is inadequate as preparation to study this topic. I most sincerely congratulate the author in having done such a superbly well organized job in writing such a highly readable book in this challenging and important topic.

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  • Anonymous

    Posted July 30, 2002

    If you're new to the topic, buy Weinstock's book instead.

    This book is overly confusing without an upfront clearly-stated goal (typical of so many advanced math books). Probably the content is okay, if you can wade through the math. It seems to be free from errors.

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  • Anonymous

    Posted July 20, 2009

    No text was provided for this review.

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