A Brief Note on Precalculus and its Function

Abstract

About the Study

Precalculus is a subject (or a combination of courses) in mathematics education that covers algebra and trigonometry at a level that is aimed to prepare students for the study of calculus. Schools frequently split algebra and trigonometry as two distinct areas of the curriculum. Students will need proficiency with algebraic expressions, particularly in the modification and transformation of such expressions, in order to obtain the derivatives and antiderivatives of calculus. Introduction in analysin infinitorum (Latin: Introduction to the Analysis of the Infinite), written by Leonhard Euler in 1748, "was aimed as an overview of concepts and techniques in analysis and analytic geometry antecedent to the study of differential and integral calculus." He began by going through the basics of variables and functions. The use of exponentiation to introduce transcendental functions is one of his innovations. Euler presents the universal logarithm as the inverse of an exponential function to any positive base.

Precalculus introduces learners for calculus in a somewhat different way than pre-algebra prepares them for algebra. While pre-algebra classes generally cover a wide range of basic algebraic ideas, precalculus courses may only teach a tiny portion of calculus concepts, if at all, and frequently include algebraic subjects that were not covered in previous algebra courses. In terms of content, certain precalculus courses may differ from others. An honors-level calculus course, for example, may devote extra attention to conic sections, Euclidean vectors, and other topics important in professions like medicine and engineering. A college preparatory/regular class could cover concepts like matrices or power functions, which are useful in business.

Another change in the present literature is the absence of complex numbers, save where they occur as roots of a quadratic equation with a negative discriminant or in Euler's formula as a trigonometric application. In his precalculus, Euler employed not just complex numbers but also infinite series. The application by Saint-Vincent to get his hyperbolic logarithm, which Euler used to finesse his precalculus, may be covered in today's course, but not the application by Saint-Vincent to acquire his hyperbolic logarithm, which Euler used to finesse his precalculus.

Functions composition, and inverse functions are commonly discussed in conjunction with sets and real numbers in a normal course. Polynomials and rational functions are developed in particular. Trigonometric functions and identities are used to practise algebraic abilities. Precalculus also covers the binomial theorem, polar coordinates, parametric equations, and the limits of sequences and series. Although the mathematical induction technique of proof for propositions using a natural number is occasionally shown, most coursework consists of exercises rather than theory.

Precalculus is a more advanced kind of secondary school algebra that is designed to prepare pupils for calculus. A review of algebra is usually included in pre-calculus, as well as an introduction to exponential, logarithmic, and trigonometric functions, as well as analytic geometry. Introduction to analysis, collegiate algebra, and trigonometry are equivalent courses.

Precalculus includes the following components in detail:

• Numbers

• Function

• Equation

• Trigonometry

Numbers

• Sets

• Complex numbers

• Real numbers

• Imaginary numbers

Function

• Properties of functions

• Composite functions

• Polynomial functions

• Rational functions

• Exponential functions

• Logarithmic functions

• Polar coordinates system

Equation

• Polynomial equations

• Parametric equations

• Differential equation

• Ordinary differential equations

• Solving equations and inequalities

• Matrices

Trigonometry

• Trigonometry

• Trigonometric functions and their function inverses

• Trigonometric identities

• Conic sections

• Sequences and Series

• Binomial theorem

• Euclidean vectors

• Mathematical induction