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Concept
Mathematical model
Summary
A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences
(such as economics, psychology, sociology, political science). It can also be taught as a subject in its own right.
The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research.
Mathematical models are also used in music, linguistics, and
philosophy (for example, intensively in analytic philosophy).
A model may help to explain a system and to study the effects of different components, and to make predictions about behavior.
Mathematical models can take many forms, including dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures. In general, mathematical models may include logical models. In many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments. Lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed.
In the physical sciences, a traditional mathematical model contains most of the following elements:
Governing equations
Supplementary sub-models
Defining equations
Constitutive equations
Assumptions and constraints
Initial and boundary conditions
Classical constraints and kinematic equations
Mathematical models are of different types:
Linear vs. nonlinear: If all the operators in a mathematical model exhibit linearity, the resulting mathematical model is defined as linear.
Official source
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