1
BASIC CALCULUS REFRESHER
Ismor Fischer, Ph.
D.
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,...
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1
BASIC CALCULUS REFRESHER
Ismor Fischer, Ph.
D.
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 http://www.
stat.
wisc.
edu/~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, (−11.
2)1
= −11.
2, (8.
6)2
= 8.
6 ×
Less