Mathematical Modeling

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
necessary