Precalculus

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.

The general logarithm, to an arbitrary positive base, Euler presents as the inverse of an exponential function.

This appropriation of the significant number from Grégoire de Saint-Vincent’s calculus suffices to establish the natural logarithm.

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.

Today's course may cover arithmetic and geometric sequences and series, but not the application by Saint-Vincent to gain his hyperbolic logarithm, which Euler used to finesse his precalculus.

For example, an honors-level course might spend more time on conic sections, Euclidean vectors, and other topics needed for calculus, used in fields such as medicine or engineering.

A college preparatory/regular class might focus on topics used in business-related careers, such as matrices, or power functions.

The binomial theorem, polar coordinates, parametric equations, and the limits of sequences and series are other common topics of precalculus.

Sometimes the mathematical induction method of proof for propositions dependent upon a natural number may be demonstrated, but generally coursework involves exercises rather than theory.