BASIC CALCULUS REFRESHER

← Back to document page

1. BASIC CALCULUS REFRESHER . Ismor Fischer, Dept. of Statistics UW-Madison 1. Introduction. This is a very condensed and simplified version of BASIC CALCULUS , which is a prerequisite for many courses in Mathematics, Statistics, Engineering, Pharmacy, etc. It is not comprehensive, and absolutely not intended to be a substitute for a one-year freshman course in differential and integral CALCULUS . You are strongly encouraged to do the included Exercises to reinforce the ideas. Important mathematical terms are in boldface; key formulas and concepts are boxed and highlighted . To (). view a color .pdf version of this document (recommended), see ~ifischer. 2. Exponents BASIC Definitions and Properties For any real number base x, we define powers of x: x0 = 1, x1 = x, x2 = x x, x3 = x x x, etc. (The exception is 00, which is considered indeterminate.) Powers are also called exponents. Examples: 50 = 1, ( )1 = , ( )2 = = , 103 = 10 10 10 = 1000, ( 3)4 = ( 3) ( 3) ( 3) ( 3) = 81.

2 ( 1.5, 0) (–1.8, 7) (0, 7) (2.5, 7) (0, 3) 0 3. Functions and Their Graphs Input x Output y If a quantity y always depends on another quantity x in such a way that every value of x corresponds to one and only one value of y, then we say that “y is a function of x,” written y = f (x); x is said to be the independent variable, y is the dependent variable.

  Their, Functions, Calculus, Graph, Functions and their graphs