英语词汇“calculus of variations”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

b. The amount by which some quantity changes in value, or the addition made to the quantity; esp. the change in a function when there is a small change in the variables or constituent functions of the function; calculus of variations, a form of calculus applicable to expressions or functions in which the law relating the quantities is liable to variation.In the calculus of variations the function concerned is usually an integral, and the aim is to find what relation between the variables in the integrand makes the integral a maximum or a minimum.

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the world > relative properties > number > calculus > [noun] > other forms of

calculus of variations1810

predicate calculus1938

the world > relative properties > number > algebra > [noun] > expression > function > value or set of values of > change in values > specific amount

increment1721

variation1810

1810 Woodhouse (title) A Treatise on Isoperimetrical Problems, and the Calculus of Variations.

1810 Woodhouse Treat. Isoperimetrical Problems iii. 45 The general form of these equations is, P.bg − Q.ci + R.dδ, dδ being a variation of the ordinate similar to the variations bg and ci.

1814 J. Toplis tr. P. S. de Laplace Treat. Analyt. Mech. ii. 46 Of all the curves along which a moving body, subjected to the forces P, Q, and R, can pass from one given point to another given point, it will describe that in which the variation of the integral ∫vds is nothing, and in which, consequently this integral is a minimum.

a1832 Encycl. Metrop. (1845) II. 209 To obtain the variation of a function of y we must write y + δy for y, and having expanded the new function according to the powers of δy, subtract from it the original function, and the first term of the difference will be the variation required.

1834 W. R. Hamilton in Philos. Trans. (Royal Soc.) 124 252 Although Lagrange and others, in treating of the motion of a system, have shown that the variation of this definite integral vanishes when the extreme coordinates and the constant H are given, they appear to have deduced from this result only the well known law of least action.

1855 D. Brewster Mem. Life I. Newton (new ed.) I. xiii. 349 The calculus of variations discovered by Lagrange in 1760, was the greatest step in the improvement of the infinitesimal calculus which was made in the last century.

1861 Todhunter (title) A History of the Progress of the Calculus of Variations during the Nineteenth Century.

1934 W. V. Houston Princ. Math. Physics v. 56 The variation of the integral is defined as its value when α has the infinitesimal value δα, minus its value when α is zero.

1972 M. Kline Math. Thought xxiv. 578 By equating the variation of the integral to zero and by using a crude limiting process to transform the resulting difference equation, he obtained the differential equation which must be satisfied by the minimizing arc.

单词	calculus of variations
释义	> as lemmas calculus of variations b. The amount by which some quantity changes in value, or the addition made to the quantity; esp. the change in a function when there is a small change in the variables or constituent functions of the function; calculus of variations, a form of calculus applicable to expressions or functions in which the law relating the quantities is liable to variation.In the calculus of variations the function concerned is usually an integral, and the aim is to find what relation between the variables in the integrand makes the integral a maximum or a minimum. ΘΚΠ the world > relative properties > number > calculus > [noun] > other forms of calculus of variations1810 predicate calculus1938 the world > relative properties > number > algebra > [noun] > expression > function > value or set of values of > change in values > specific amount increment1721 variation1810 1810 Woodhouse (title) A Treatise on Isoperimetrical Problems, and the Calculus of Variations. 1810 Woodhouse Treat. Isoperimetrical Problems iii. 45 The general form of these equations is, P.bg − Q.ci + R.dδ, dδ being a variation of the ordinate similar to the variations bg and ci. 1814 J. Toplis tr. P. S. de Laplace Treat. Analyt. Mech. ii. 46 Of all the curves along which a moving body, subjected to the forces P, Q, and R, can pass from one given point to another given point, it will describe that in which the variation of the integral ∫vds is nothing, and in which, consequently this integral is a minimum. a1832 Encycl. Metrop. (1845) II. 209 To obtain the variation of a function of y we must write y + δy for y, and having expanded the new function according to the powers of δy, subtract from it the original function, and the first term of the difference will be the variation required. 1834 W. R. Hamilton in Philos. Trans. (Royal Soc.) 124 252 Although Lagrange and others, in treating of the motion of a system, have shown that the variation of this definite integral vanishes when the extreme coordinates and the constant H are given, they appear to have deduced from this result only the well known law of least action. 1855 D. Brewster Mem. Life I. Newton (new ed.) I. xiii. 349 The calculus of variations discovered by Lagrange in 1760, was the greatest step in the improvement of the infinitesimal calculus which was made in the last century. 1861 Todhunter (title) A History of the Progress of the Calculus of Variations during the Nineteenth Century. 1934 W. V. Houston Princ. Math. Physics v. 56 The variation of the integral is defined as its value when α has the infinitesimal value δα, minus its value when α is zero. 1972 M. Kline Math. Thought xxiv. 578 By equating the variation of the integral to zero and by using a crude limiting process to transform the resulting difference equation, he obtained the differential equation which must be satisfied by the minimizing arc. extracted from variationn. < as lemmas
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