Mathematics Cheat Sheet For Population Biology
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9Mathematics Cheat Sheet for Population Biology
James Holland Jones,
Department of Anthropological Sciences
Stanford University
April 30, 2008
1
Introduction
If you fake it long enough, there comes a point where you aren’t faking it any more. Here are
some tips to help you along the way...
2
Calculus
Derivative The definition of a derivative is as follows. For some function f (x),
f (x + h)
f (x)
f (x) = lim
.
h
h
0
2.1
Differentiation Rules
It is useful to remember the following rules for differentiation. Let f (x) and g(x) be two functions
2.1.1
Linearity
d
(af (x) + bg(x)) = af (x) + bg (x)
dx
for constants a and b.
2.1.2
Product rule
d
(f (x)g(x)) = f (x)g(x) + f (x)g (x)
dx
2.1.3
Chain rule
d
g(f (x)) = g (f (x))f (x)
dx
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