A branch of mathematics which is a sort of generalization of Calculus. Calculus of variations seeks to find the path, curve, surface, etc., for which a given Function has a Stationary Value (which, in physical problems, is usually a Minimum or Maximum). Mathematically, this involves finding Stationary Values of integrals of the form

*I* has an extremum only if the Euler-Lagrange Differential Equation is satisfied, i.e., if

The Calculus of Variations Fundamental Lemma states that, if

with Continuous second Partial Derivatives, then

on (*a*,*b*).

*See also * Beltrami Identity, Bolza Problem, Brachistochrone Problem , Catenary, Envelope
Theorem, Euler-Lagrange Differential Equation, Isoperimetric Problem, Isovolume Problem,
Lindelof's Theorem, Partition Calculus,
Plateau's
Problem, Roulette, Skew Quadrilateral, Sphere with Tunnel, Unduloid,
Weierstraß-Erdman Corner Condition

**References**

© 1996-7

Mon Feb 17 13:44:27 EST 1997

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