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© 2014 Pacific Crest
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Not starting with a simple model
Example
: Modeling population dynamics becomes very chaotic when no simplifications are
made.
Why?
While a simplified model for population dynamics often produces accurate results,
attempts to include all features of the ecology lead to chaotic systems with no stable
solutions.
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Finding a solution the hard way
Example
: Adding up the terms in a series 1 + 2 + 3 +…+
n
Why?
You should not add the numbers in the series one by one, rather use the formula
( 1)
2
n n
+
.
(See also, inadequate background knowledge and reinventing the wheel.)
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Failing to reframe the problem
Example
: Raw data used instead of scaled data
Why?
You create a mathematical model where your input variable is the number of years
after 2000. When using the model you input the calendar year instead and receive an
incorrect output.
A
re You Ready?
Before continuing, you should be able to ...
I can...
OR
Here’s my question...
identify the set of all characteristics in a
situation and differentiate between those
important enough to be included in the
model and those insignificant enough to
omit
identify the relationships and patterns
used in abstracting a model
explain the steps of the methodology for
constructing a mathematical model
9.2 Constructing a Mathematical Model