Description
Book SynopsisThere is a deep and fundamental relationship between the differential equations that occur in the calculus of variations and partial differential equations of the first order: in particular, to each such partial differential equation there correspond variational problems. This book discusses this basic fact.
Table of ContentsContinuous convergence, implicit functions, ordinary differential equations Fields of curves and multidimensional surfaces, complete systems Partial differential equations of the first order, theory of characteristics Poisson brackets, systems of partial differential equations of the first order Elements of tensor calculus Canonical transformations Contact transformations The Pfaff problem Function groups The integration theories of Lagrange, Jacobi, Adolph Mayer and Lie Ordinary maxima and minima. Quadratic forms Simple variational problems in the small Variational problems in parametric representation Positive-definite variational problems Quadratic variational problems. Theory of the second variation The boundary-value problem and the question of the absolute minimum Closed extremals. Periodic variational problems The problem of Lagrange Guide to the literature Index.
