Editing Mathematical analysis (section)

== Applications ==
Techniques from analysis are also found in other areas such as:

=== Physical sciences ===
The vast majority of [[classical mechanics]], [[Theory of relativity|relativity]], and [[quantum mechanics]] is based on applied analysis, and [[differential equation]]s in particular. Examples of important differential equations include [[Newton's second law]], the [[Schrödinger equation]], and the [[Einstein field equations]].

[[Functional analysis]] is also a major factor in [[quantum mechanics]].

=== Signal processing ===
When processing signals, such as [[Sound|audio]], [[radio wave]]s, light waves, [[seismic waves]], and even images, Fourier analysis can isolate individual components of a compound waveform, concentrating them for easier detection or removal.  A large family of signal processing techniques consist of Fourier-transforming a signal, manipulating the Fourier-transformed data in a simple way, and reversing the transformation.<ref>{{cite book |title=Theory and Application of Digital Signal Processing |last1=Rabiner |first1=L. R. |last2=Gold |first2=B. |location=Englewood Cliffs, New Jersey |publisher=[[Prentice-Hall]] |date=1975 |isbn=978-0139141010 |url=https://archive.org/details/theoryapplicatio00rabi |url-access=registration}}</ref>

=== Other areas of mathematics ===
Techniques from analysis are used in many areas of mathematics, including:
* [[Analytic number theory]]
* [[Analytic combinatorics]]
* [[Continuous probability]]
* [[Differential entropy]] in information theory
* [[Differential game]]s
* [[Differential geometry]], the application of calculus to specific mathematical spaces known as [[manifold]]s that possess a complicated internal structure but behave in a simple manner locally.
* [[Differentiable manifolds]]
* [[Differential topology]]
* [[Partial differential equations]]