Neue Rechnungsmethoden der Höheren Mathematik Neue Integrationsmethoden auf Grund der Potenzial-, Logarithmal-, und Numeralrechnung

Abstract

THE first of these pamphlets contains an account of what the author calls the Immensalrechnung, the Potenzialrechnung, the Radikalrechnung, the Logarithmalrechnung, and the Numeralrechnung. In the Immensalrechnung an attempt is made to provide a calculus of the infinitely great (das Immensal), which shall form a complement to the differential calculus, or calculus of the infinitely small. The Potenzialrechnung contains an account of exponential functions in which the base is an infinitely small or an infinitely great quantity, and the exponent is infinitely small; and the Radikalrechnung an account of the inverse functions that are obtained from these by changing the exponent into its reciprocal. So, too, in the Logarithmalrechnung, logarithmic functions are considered in which the base and the argument are either infinitely small or infinitely great; and in the Numeralrechnung the inverse functions (antilogarithms or exponential functions) are discussed. The pamphlet is occupied, for the most part, with an exposition of the author's notation, a discussion of certain indeterminate forms, and a calculation of some algebraic functions containing an infinitely small argument, to a first, second, or third approximation. It is hardly possible to compliment the author on his accuracy, seeing that the statement occurs that Lt.logx is finite when x is zero or infinity, the reason given being that Lt.(xlogx) and Lt.(log x/x) are zero, for these values of x.