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

Dennis M. Cates ()

Chapter Chapter 8 in Cauchy's Calcul Infinitésimal, 2019, pp 37-41 from Springer

Abstract: 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.

Date: 2019
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DOI: 10.1007/978-3-030-11036-9_8

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