MATHEMATICAL MODEL

either of two decidedly different kinds of mathematical representation. Physical mathematical models include reproductions of plane and solid geometric figures made of cardboard, wood, plastic, or other substances; models of conic sections, curves in space, or three-dimensional surfaces of various kinds made of wire, plaster, or thread strung from frames; and models of surfaces of higher order that make it possible to visualize abstract mathematical concepts. The usage of the term in the theoretical or analytical sense denotes, perhaps, the more important kind of model. Essentially, any real situation in the physical and biological world, whether natural or involving technology and human intervention, is subject to analysis by modeling if it can be described in terms of mathematical equations. Thus, optimization and control theory may be used to model industrial processes, traffic patterns, sediment transport in streams, and other situations; information and communication theory may be used to model message transmission, linguistic characteristics, and the like; and dimensional analysis and computer simulation may be used to model atmospheric circulation patterns, stress distribution in engineering structures, the growth and development of landforms, and a host of other processes in science and engineering.