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DIFFERENTIALS OF FUNCTIONS OF SEVERAL VARIABLES. PARTIAL DERIVATIVES AND PARTIAL DIFFERENTIALS.

  • Dennis M. CatesEmail author
Chapter

Abstract

Let \(u=f(x, y, z, \dots ) \) be a function of several independent variables \( x, y, \) \( z, \dots . \ \) We denote by i an infinitely small quantity, and by
$$\begin{aligned}&\varphi (x, y, z, \dots ), \\&\chi (x, y, z, \dots ), \\&\psi (x, y, z, \dots ), \\&\ \ \dots \dots \dots \dots \end{aligned}$$
the limits toward which the ratios
$$\begin{aligned}&\frac{f(x+i, y, z, \dots )-f(x, y, z, \dots )}{i}, \\&\frac{f(x, y+i, z, \dots )-f(x, y, z, \dots )}{i}, \\&\frac{f(x, y, z+i, \dots )-f(x, y, z, \dots )}{i}, \\&\ \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \end{aligned}$$
converge, while i indefinitely approaches zero.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Sun CityUSA

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