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

(1) |

(2) |

(3) |

(4) |

**References**

Arfken, G. ``Calculus of Variations.'' Ch. 17 in *Mathematical Methods for Physicists, 3rd ed.*
Orlando, FL: Academic Press, pp. 925-962, 1985.

Bliss, G. A. *Calculus of Variations.* Chicago, IL: Open Court, 1925.

Forsyth, A. R. *Calculus of Variations.* New York: Dover, 1960.

Fox, C. *An Introduction to the Calculus of Variations.* New York: Dover, 1988.

Isenberg, C. *The Science of Soap Films and Soap Bubbles.* New York: Dover, 1992.

Menger, K. ``What is the Calculus of Variations and What are Its Applications?'' In
*The World of Mathematics* (Ed. K. Newman). Redmond, WA: Microsoft Press, pp. 886-890, 1988.

Sagan, H. *Introduction to the Calculus of Variations.* New York: Dover, 1992.

Todhunter, I. *History of the Calculus of Variations During the Nineteenth Century.* New York: Chelsea, 1962.

Weinstock, R. *Calculus of Variations, with Applications to Physics and Engineering.* New York: Dover, 1974.

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1999-05-26