calculus of variations

noun

1. the branch of mathematics that deals with the problem of finding a curve or surface that maximizes or minimizes a given expression, usually with several restrictions placed on the desired curve.

calculus of variations

noun

1. a branch of calculus concerned with maxima and minima of definite integrals

calculus of variations

1. Mathematical analysis of the maxima and minima of definite integrals, the integrands of which are functions of independent variables, dependent variables, and the derivatives of one or more dependent variables.

2. Compare differential calculus integral calculus

Word History and Origins

Origin of calculus of variations¹

First recorded in 1830–40

Example Sentences

Her 1913 result on the calculus of variations, leading to Noether’s Theorem is considered one of the most important theorems in mathematics—and one that shaped modern physics.

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Some problems are ill-posed: the fourth problem is sometimes described as “too vague to have a solution,” and the 23rd problem is just “Further development of the methods of the calculus of variations.”

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He is an expert on calculus of variations and partial differential equations.

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Little in mathematics beyond the elementary level of calculus of variations, and nothing at all about Banach algebra or Riemannian manifolds.

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Furthermore it can be shown by the application of the calculus of variations that the condition for a minimum value of the function W, is that ∇V = 0.

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