Euler used not only complex numbers but also infinite series in his precalculus. Another difference in the modern text is avoidance of complex numbers, except as they may arise as roots of a quadratic equation with a negative discriminant, or in Euler's formula as application of trigonometry. An exposition on compound interest in financial mathematics may motivate this limit. Then the natural logarithm is obtained by taking as base "the number for which the hyperbolic logarithm is one", sometimes called Euler's number, and written e. The general logarithm, to an arbitrary positive base, Euler presents as the inverse of an exponential function. His innovation is noted for its use of exponentiation to introduce the transcendental functions. Leonhard Euler wrote the first precalculus book in 1748 called Introductio in analysin infinitorum ( Latin: Introduction to the Analysis of the Infinite), which "was meant as a survey of concepts and methods in analysis and analytic geometry preliminary to the study of differential and integral calculus." He began with the fundamental concepts of variables and functions. For students to succeed at finding the derivatives and antiderivatives of calculus, they will need facility with algebraic expressions, particularly in modification and transformation of such expressions.
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