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.
Leonhard Euler
wrote the first precalculus book in 1748 called
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."
[2]
He began with the
fundamental concepts of
variables
and
functions
. His innovation is noted for its use
of
exponentiation
to introduce the
transcendental functions
. The general logarithm, to an arbitrary
positive base, Euler presents as the inverse of an
exponential function
.
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
. This appropriation of the
significant number from
Gregoire de Saint-Vincent