Mathematical Modeling and Analysis

mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physicsbiologyearth sciencechemistry) and engineering disciplines (such as computer scienceelectrical engineering), as well as in non-physical systems such as the social sciences (such as economicspsychologysociologypolitical science). 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.

Analysis is the branch of mathematics dealing with limits and related theories, such as differentiationintegration,measuresequencesseries, and analytical functions.

These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space).

 

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