Calculus of Variations

by Israel M. Gelfand, S.V. Fomin, Richard A. Silverman (Translator)

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 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 seven considers the application of variational methods to the study of systems with infinite degrees of freedom, and Chapter eight 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 ne edition will be welcomed by advanced undergraduate and graduate students of mathematics and physics.

Genres: Mathematics, Reference, Textbooks, Calculus, Science

256 pages, Paperback

First published January 1, 1963

About the author

Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand (Yiddish: ישראל געלפֿאַנד‎, Russian: Израиль Моисеевич Гельфанд ; 2 September [O.S. 20 August] 1913 – 5 October 2009) was a prominent Soviet mathematician. He made significant contributions to many branches of mathematics, including group theory, representation theory and functional analysis. The recipient of many awards, including the Order of Lenin and the Wolf Prize, he was a Fellow of the Royal Society and professor at Moscow State University and, after immigrating to the United States shortly before his 76th birthday, at Rutgers University.

Reviews

[Ben · Rating 4 out of 5]

Chapter 1 does provide an excellent general overview, but you dont get to the meat (read: actual necessary and sufficient conditions for extrema) until chapter 6. Personally I would have put them much earlier.

[David · Rating 4 out of 5]

This is a great introduction to the calculus of variations. It's mathematically rigorous while not being long-winded.

[Nick Black]

OH SHIT, THERE'S A HORSE IN THE HOSPITAL

[Henrique Felipe · Rating 5 out of 5]

Em minha opinião, é o melhor livro de cálculo variacional que existe. O conteúdo é muito bom, porém é voltado para quem tem uma boa base em cálculo e equações diferenciais ordinárias e parciais.

[Moataz Elmasry · Rating 4 out of 5]

Concise, clear, and covers all the key calculus of variations topics.