英和和英

名詞

the calculus of variations (uncountable)

1. (calculus) The form of calculus that deals with the maxima and minima of definite integrals of functions of many variables.
   • 1885, Lewis Buffett Carll, A Treatise on the Calculus of Variations, Macmillan and Co., page 550:

     The next advance was made by Cauchy in a memoir on the calculus of variations published in the third volume of his Exercices d'analyse et de Physique Mathématique, 1844, extending from page 50 to page 130.

   • 2004, Bernard Dacorogna, Introduction to the Calculus of Variations, 2nd Edition, Imperial College Press, page 2,

     In the nineteenth century and in parallel to some of the work that was mentioned above, probably, the most celebrated problem of the calculus of variations emerged, namely the study of the Dirichlet integral; a problem of multiple integrals.

   • 2023, Filippo Santambrogio, A Course in the Calculus of Variations, Springer, page 57:

     On the other hand, we can also consider that the calculus of variations includes all optimization problems where the unknown are functions […] .

Further reading

• Fundamental lemma of calculus of variations on Wikipedia.Wikipedia
• Euler–Lagrange equation on Wikipedia.Wikipedia
• Functional (mathematics) on Wikipedia.Wikipedia
• Functional derivative on Wikipedia.Wikipedia