Calculus of Variations

<p>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.<br>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.<br>Substantially revised and corrected by the translator this inexpensive new edition will be welcomed by advanced undergraduate and graduate students of mathematics and physics.