Mathematics Describing the Real World: Precalculus and Trigonometry

Precalculus is important preparation for calculus; it also draws on algebra, trigonometry and other topics; the essential concept of the function; trying hand at simple problems; Professor Edwards's recommendations for approaching the series.

The most common type of algebraic function is a polynomial function; linear and quadratic functions; different techniques for finding roots; a valuable tool is the intermediate value theorem; it identifies real-number roots for polynomial functions.

The world of complex numbers, where i is defined as the square root of -1; learning how to calculate and find roots of polynomials using complex numbers; how certain complex expressions produce beautiful fractal patterns when graphed.

Rational functions are quotients of polynomials; finding the domain of the function; recognizing the vertical and horizontal asymptotes, both by graphing and comparing the values of the numerator and denominator; applications of rational functions.

Functions can be combined in ways including addition, multiplication and composition; the inverse function has important applications; recognizing inverse functions on a graph; the function and its inverse form mirror images across the line y = x.

Using inequalities to express the set of values in the domain of a function; the notation for inequalities; how to represent inequalities on graphs; techniques to solve inequalities; those involving absolute value, which occur frequently in calculus.