CALCULUS OF VARIATIONS, I. M. GELFAND, S. V. FOMIN

 CALCULUS OF VARIATIONS,  I. M. GELFAND,  S. V. FOMIN 

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 compre hensive course on the elements of the calculus of varia tions,-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 f inite 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 treat ment of direct methods in the calculus of variations. 

Topics are discussed in this book:

• ELEMENTS OF THE THEORY 
• FURTHER GENERALIZATIONS
• THE GENERAL VARIATION OF A FUNCTIONAL 
• THE CANONICAL FORM OF THE EULER EQUA TIONS AND RELATED TOPICS
• THE SECOND VARIATION. SUFFICIENT CONDI TIONS FOR A WEAK EXTREMUM 
• FIELDS. SUFFICIENT CONDITIONS FOR A STRONG EXTREMUM
• VARIATIONAL PROBLEMS INVOLVING MULTIPLE INTEGRALS 
• DIRECT METHODS IN THE CALCULUS OF VARIATIONS  

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