Calculus of Variations: With Supplementary Notes and Exercises, 1945-1946Courant Institute of Mathematical Sciences, New York University, 1962 - Calculus of variations - 281 pages |
From inside the book
85 pages matching Calculus of Variations in this book
Where's the rest of this book?
Results 1-3 of 85
Other editions - View all
Calculus of Variations and Supplementary Notes and Exercises: Lectures, 1945 ... Richard Courant No preview available - 1957 |
Common terms and phrases
admissible functions arbitrary arc length assume boundary condition boundary value problem calculus of variations conjugate point consider constant continuous function coordinate system corresponding curve d₂ defined denote dependent difference quotients Dirichlet's Principle distance dxdy eigenvalue endpoint equa equicontinuous Euler equation Euler expression example exists extremal integral extremum family of extremals field finite number fixed follows geodesics given greatest lower bound Hamilton-Jacobi equation Hamiltonian harmonic function Hence homogeneous implies independent variables inequality invariance isoperimetric problem lattice points Legendre transformation linear method minimizing sequence minimum problem necessary condition neighborhood obtain P₁ parameter family partial derivatives partial differential equation piecewise continuous plane polar coordinates prescribed proof prove respect satisfy semi-continuity side condition solution solved straight line segment surface t₁ t₂ theorem theory tion transversality condition u₁ upper bound v₁ vanish variational problem vector Weierstrass zero