Precalculus
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In mathematics education, precalculus is a course, or a set of courses, that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus, thus the name precalculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework.[1]
Concept
For students to succeed at finding the
antiderivatives with 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 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."[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
Euler's number
, and written . This appropriation of the significant number from 
Gregoire de Saint-Vincent
’s calculus suffices to establish the natural logarithm. This part of precalculus prepares the student for integration of the monomial in the instance of .
Today's precalculus text computes as the limit . An exposition on
infinite series
in his precalculus. 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.
Variable content
Precalculus prepares students for calculus somewhat differently from the way that
power functions
.
A standard course considers
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.
Sample texts
- Roland E. Larson & Robert P. Hostetler (1989) Precalculus, second edition, ISBN 0-669-16277-9
- Margaret L. Lial & Charles D. Miller (1988) Precalculus, ISBN 0-673-15872-1
- Jerome E. Kaufmann (1988) Precalculus, PWS-Kent Publishing Company (Wadsworth)
- Karl J. Smith (1990) Precalculus Mathematics: a functional approach, fourth edition, ISBN 0-534-11922-0
- Michael Sullivan (1993) Precalculus, third edition, Dellen imprint of ISBN 0-02-418421-7
Online access
- Jay Abramson and others (2014) Precalculus from OpenStax
- David Lippman & Melonie Rasmussen (2017) Precalculus: an investigation of functions
- Carl Stitz & Jeff Zeager (2013) Precalculus (pdf)
See also
- Education portal
Mathematics portal
References
- ^ Cangelosi, J. S. (2012). Teaching mathematics in secondary and middle school, an interactive approach. Prentice Hall.
- ISBN 0-7156-1295-6.
External links
Look up precalculus in Wiktionary, the free dictionary.
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