Applied mathematics

== History ==
[[File:Elmer-pump-heatequation.png|thumb|right|A numerical solution to the [[heat equation]] on a pump casing model using the [[finite element method]].]]

Historically, applied mathematics consisted principally of [[Mathematical analysis|applied analysis]], most notably [[differential equations]]; [[approximation theory]] (broadly construed, to include [[Representation (mathematics)|representation]]s, [[Asymptotic analysis|asymptotic]] methods, [[Calculus of variations|variational methods]], and [[numerical analysis]]); and applied [[probability]]. These areas of mathematics related directly to the development of [[Newtonian physics]], and in fact, the distinction between mathematicians and physicists was not sharply drawn before the mid-19th century. This history left a pedagogical legacy in the United States: until the early 20th century, subjects such as [[classical mechanics]] were often taught in applied mathematics departments at American universities rather than in [[physics]] departments, and [[fluid mechanics]] may still be taught in applied mathematics departments.<ref name="Stolz2002">
{{citation|author=Stolz, M.|title=The History Of Applied Mathematics And The History Of Society|journal=Synthese|volume=133|issue=1|pages=43–57|year=2002|doi=10.1023/A:1020823608217|s2cid=34271623}}</ref> [[Engineering]] and [[computer science]] departments have traditionally made use of applied mathematics.

As time passed, Applied Mathematics grew alongside the advancement of science and technology. With the advent of modern times, the application of mathematics in fields such as science, economics, technology, and more became deeper and more timely. The development of computers and other technologies enabled a more detailed study and application of mathematical concepts in various fields.

Today, Applied Mathematics continues to be crucial for societal and technological advancement. It guides the development of new technologies, economic progress, and addresses challenges in various scientific fields and industries. The history of Applied Mathematics continually demonstrates the importance of mathematics in human progress.