Theses on the Calculus of Variations Submitted to the Faculty of the Division of the Physical Sciences in Candidacy for the Degree of Doctor of Philosophy, Department of Mathematics ...1933 - Calculus of variations - 426 pages |
Contents
TABLE OF CONTENTS | 3 |
MAX CORAL THE EULERLAGRANGE MULTIPLIER RULE | 63 |
RALPH AUBRIE Hefner The CONDITION OF Mayer for DISCON | 95 |
14 other sections not shown
Common terms and phrases
admissible arc admissible variations analogue arguments boundary value problem C₂ calcolo delle variazioni calculus of variations characteristic numbers coefficients conjugate point constants continuous corner corollary corresponding curve deduced defined definition determinant different from zero differential equations discontinuities double integral E₁₂ end conditions exists expression extremaloid finite number Fischer focal point follows Fréchet func functional F functions of lines funzioni given Hence hypotheses identically zero inequality interval isoperimetric problems Jacobi condition Lagrange problem Lemma Lincei linear functional linearly independent manifold matrix maximizing arc minimizing arc minimizing surface minimum monopoly problem necessary condition neighborhood normal parameter values partial derivatives problem of Lagrange problem of Mayer problem of minimizing proof properties quadratic form respect Riesz Riesz theorem satisfying the conditions second variation semi-extremal Stieltjes integral Stourgeon sufficient conditions surface theorem tions Tonelli vanish variable Volterra derivative x₂ y₁