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DIFFERENTIALS OF ANY FUNCTION OF SEVERAL VARIABLES EACH OF WHICH IS IN ITS TURN A LINEAR FUNCTION OF OTHER SUPPOSED INDEPENDENT VARIABLES. DECOMPOSITION OF ENTIRE FUNCTIONS INTO REAL FACTORS OF FIRST OR OF SECOND DEGREE.

  • Dennis M. CatesEmail author
Chapter

Abstract

Let \( a, b, c, \dots , k \) be constant quantities, and let
$$\begin{aligned} u=ax+by+cz+\cdots +k \end{aligned}$$
be a linear function of the independent variables \( x, y, z, \dots . \ \) The differential
$$\begin{aligned} du=a dx+b dy+c dz+\cdots \end{aligned}$$
will itself be a constant quantity, and as a result, the differentials \( d^2u, \) \( d^3u, \) \(\dots \) will all be reduced to zero. We immediately conclude from this remark that the successive differentials of the functions
$$\begin{aligned} f(u), \ \ \ f(u, v), \ \ \ f(u, v, w, \dots ), \ \ \ \dots \end{aligned}$$

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Sun CityUSA

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