## Calculus of VariationsBased 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. |

### Contents

ELEMENTS OF THE THEORY | 1 |

FURTHER GENERALIZAT1ONS | 34 |

THE GENERAL VARIATION OF A FUNCTIONAL | 54 |

THE CANONICAL FORM OF THE EULER EQUATIONS AND RELATED TOPICS | 67 |

THE SECOND VARIATION SUFFICIENT CONDITIONS FOR A WEAK EXTREMUM | 97 |

FIELDS SUFFICIENT CONDITIONS FOR A STRONG EXTREMUM | 131 |

VARIATIONAL PROBLEMS INVOLVING MULTIPLE INTEGRALS | 152 |

DIRECT METHODS IN THE CALCULUS OF VARIATIONS | 192 |