Mathematical Modeling

Topics: Mathematics, Mathematical model, Chaos theory Pages: 3 (728 words) Published: March 26, 2007
Mathematical modeling is commonly used to predict the
behavior of phenomena in the environment. Basically,
it involves analyzing a set of points from given data
by plotting them, finding a line of "best fit" through
these points, and then using the resulting graph to
evaluate any given point. Models are useful in
hypothesizing the future behavior of populations,
investments, businesses, and many other things that
are characterized by fluctuations. A mathematical
model usually describes a system by a set of variables
and equations which form the basis of the
relationships between the variables.

The variables represent independent and dependent
properties of the system. Models are classified in a
variety of ways. One of these ways is "linear versus
nonlinear." A linear model is any system whose
behavior can be explained or predicted using a linear
equation or an entire set of linear equations. On the
other hand, a nonlinear model uses at least one
nonlinear equation to describe its behavior. Models
may also be classed as either deterministic or
probabilistic. A deterministic model always performs
the same way under a given set of initially occurring
conditions, while a probabilistic model is
characterized by randomness. Another way of evaluating
models is to determine whether it is static or
dynamic. Static models do not account for time, while
dynamic models do take this element into
consideration. In calculus, dynamic models are often
represented using differential equations. Finally,
models can have lumped parameters or distributed
parameters. A model with lumped parameters has a
consistent state throughout the system and are said to
be homogenous. A model with distributed parameters has
a changing state throughout the system. It is said to
be heterogeneous.

Another way of understanding models is to figure out
if the given model is a "white box" or a "black box"
model. White box models are constructed with all...
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