Titlebook: Cauchy‘s Calcul Infinitésimal; An Annotated English Dennis M. Cates Book 2019 Springer Nature Switzerland AG 2019 Cauchy.Calculus.Infinites

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DERIVATIVES OF FUNCTIONS OF A SINGLE VARIABLE.When the function . remains continuous between two given limits of the variable .,  and that we assign to this variable a value contained between the two limits in question, an infinitely small increment attributed to the variable produces an infinitely small increment of the function itself.

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DIFFERENTIALS OF FUNCTIONS OF A SINGLE VARIABLE.Let . always be a function of the independent variable .,  . an infinitely small quantity and . a finite quantity. If we set . . will also be an infinitely small quantity, and we will have identically

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DIFFERENTIALS OF FUNCTIONS OF SEVERAL VARIABLES. PARTIAL DERIVATIVES AND PARTIAL DIFFERENTIALS.Let . be a function of several independent variables . . We denote by . an infinitely small quantity, and by .the limits toward which the ratios .converge, while . indefinitely approaches zero.

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DIFFERENTIALS OF ANY FUNCTION OF SEVERAL VARIABLES EACH OF WHICH IS IN ITS TURN A LINEAR FUNCTION OFLet . be constant quantities, and let .be a linear function of the independent variables . The differential .will itself be a constant quantity, and as a result, the differentials . . . will all be reduced to zero. We immediately conclude from this remark that the successive differentials of the functions

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Professor in Aachen (1905–1910)ms of values of . that work to make the total differential in question vanish, must change another total differential of even order into a quantity affected by the sign that maintains the first differential, as long as it does not vanish.

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CONDITIONS WHICH MUST BE FULFILLED FOR A TOTAL DIFFERENTIAL TO NOT CHANGE SIGN WHILE WE CHANGE THE Vms of values of . that work to make the total differential in question vanish, must change another total differential of even order into a quantity affected by the sign that maintains the first differential, as long as it does not vanish.

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experience Cauchy‘s original, complete text on calculus.ProThis book is a complete English translation of Augustin-Louis Cauchy‘s historic 1823 text (his first devoted to calculus), .Résumé des le.ç.ons sur le calcul infinit.é.simal., "Summary of Lectures on the Infinitesimal Calculus," originally

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