| 单词 | exact differential |
| 释义 | > as lemmasexact differential b. Calculus. exact differential, a linear differential function of two or more variables that is equal to the total differential of some function of those variables. Also exact (differential) equation (see quot. 1959). ΚΠ 1825 D. Lardner Elem. Treat. Differential & Integral Calculus ii. xvii. 284 As there are many differentials of two variables which are not exact differentials, so also there are many differential equations which are not the immediate differentials of any primitive equation. 1877 B. Williamson Elem. Treat. Integral Calculus (ed. 3) vi. 143 Condition that Pdx + Qdy shall be a total Differential.—This implies that Pdx + Qdy should be the exact differential of some function of x and y. 1920 H. T. H. Piaggio Elem. Treat. Differential Equations ii. 12 The expression ydx + xdy is an exact differential. Thus the equation ydx + xdy = o..is called an exact equation. 1958 Van Nostrand's Sci. Encycl. (ed. 3) 511/1 Suppose that an integrating factor, v exists so that vL(u)dx is an exact differential. 1959 G. James & R. C. James Math. Dict. (ed. 2) 116/1 Exact differential equation, a differential equation which is obtained by setting the total differential of some function equal to zero. < as lemmas |
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