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Some processes are so simple that they can be described in terms of
algebraic equations, either explicitly, or implicitly as the solution
to a differential equation.
Algebraic equations are usually defined by applying some law of physics
like conservation of mass or conservation of momentum or a time or
space dependent equation describing the temporal movement of something.
For example this is an explicit algebraic model:
where is today's date. An example of an implicit algebraic equation
is the description of the time course of binding of drug to a receptor.
The dynamics is best characterized by a differential equation (equating
changes in the fraction of bound receptors to the difference between
rates of forming and unforming bound receptors) which has a simple
algebraic solution:
where is the fraction of bound receptors, is the rate of making
bound receptors, is the rate of unmaking bound receptors and
is time.
Algebraic
models are usually easy to explore because we can simple generate a sequence of
values for the independent variable and plot the resulting values of the
model's dependent variable.
Next: Ordinary Differential Equations
Up: How to create a
Previous: Reverse Engineering
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Frank Starmer
20040519
 