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Applications Techniques from analysis are also found in other areas such as: Physical sciences The vast majority of classical mechanics, relativity, and quantum mechanics is based on applied analysis, and differential equations 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 audio, radio waves, light waves, seismic waves, and even images, Fourier analysis can isolate individual components of a compound waveform, concentrating them for easier detection and/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.[19] Other areas of math Techniques from analysis are used in many areas of mathematics, including: Analytic number theory Analytic combinatorics Continuous probability Differential entropy in information theory Differential games Differential geometry, the application of calculus to specific mathematical spaces known as manifolds that possess a complicated internal structure but behave in a simple manner locally. Differential topology |
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