Calculus of Variations·I·M·Gelfand S·V·Fomin

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Calculus of Variations

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Excerpt from preface for correct understanding of the book: <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. The first three chapters, taken together, form a more comprehensive course on the elements of the calculus of variations,-but one which is still quite elementary (involving only necessary conditions for extrema) . The first six chapters contain, more or less, the material given in the usual university course in the calculus of variations (with applications to the mechanics of systems with a finite number of degrees of freedom), including the theory of fields (presented in a somewhat novel way) and sufficient conditions for weak and strong extrema. Chapter 7 is devoted to the application of variational methods to the study of systems with infinitely many degrees of freedom. Chapter 8 contains a brief treatment of direct methods in the calculus of variations.