Mathematical models are a way of analyzing systems by using equations (mathematical language) to determine how the system changes from one state to the next (usually using differential equations) and/or how one variable depends on the value or state of other variables. Simply put (although working through the equations is not always simple), the process of mathematical modeling includes the input of data and information, a way of processing the information, and an output of results.

A mathematical model can describe the behavior of many systems, including systems in the fields of biology, economics, social science, electrical and mechanical engineering, and thermodynamics. For example, modeling is usually used in the sciences to better understand physical phenomena; each phenomenon is translated into a set of equations that describe it. But don’t think that all the results of models are indicative of the real world. Because it is virtually impossible to describe a phenomenon totally, models are considered to be merely a human construct to help us better understand our surrounding real-world systems.