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.
