Applied mathematics is the application of mathematical theories and methods in fields other than core mathematics such as engineering, medicine, physics, biology, business, computer science, industry, finance, etc. Hence, it can be considered a portmanteau of mathematical science and specialized knowledge.
The term is also used to describe the specialization in the field of mathematics in which mathematicians work on practical problems by means of formulating and studying mathematical models. In the past, practical applications were used to motivate the development of mathematical theories, which later became the subject of study in pure mathematics. Abstract concepts began being studied for their own sake. The activity of applied mathematics is hence can be said to be intimately connected with research in pure mathematics.
This branch of mathematics used to consist primarily of applied analysis, mostly differential equations; approximation theory, and applied probability which were directly related to the development of Newtonian physics. It went as far as to bring out the distinction between mathematicians and physicists, which was not sharply drawn before the mid-19th century. This divide kept increasing until the early 20th century when subjects such as classical mechanics and fluid dynamics began being taught in applied mathematics departments instead of in physics departments. Engineering and computer science departments have also traditionally used applied mathematics.
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