«Դիֆերենցիալ հավասարումներ»–ի խմբագրումների տարբերություն

Յուրաքանչյուր ոչ զրոյական <math>f_{n}(x)</math>-ի համար, եթե <math>\{f_{0},f_{1},\cdots\}</math> և <math>g</math> անընդհատ են <math>x_{0}</math> պարունակող միջակայքի վրա , ապա <math>y</math> գոյություն ունի և եզակի է։<ref>{{cite book|last1=Zill|first1=Dennis G.|title=A First Course in Differential Equations|publisher=Brooks/Cole|isbn=0-534-37388-7|edition=5th|year=2001}}</ref>

== Կիրառություններ ==

 

Many fundamental laws of physics and chemistry can be formulated as differential equations. In biology and economics, differential equations are used to model the behavior of complex systems. The mathematical theory of differential equations first developed together with the sciences where the equations had originated and where the results found application. However, diverse problems, sometimes originating in quite distinct scientific fields, may give rise to identical differential equations. Whenever this happens, mathematical theory behind the equations can be viewed as a unifying principle behind diverse phenomena. As an example, consider the propagation of light and sound in the atmosphere, and of waves on the surface of a pond. All of them may be described by the same second-order partial differential equation, the wave equation, which allows us to think of light and sound as forms of waves, much like familiar waves in the water. Conduction of heat, the theory of which was developed by Joseph Fourier, is governed by another second-order partial differential equation, the heat equation. It turns out that many diffusion processes, while seemingly different, are described by the same equation; the Black–Scholes equation in finance is, for instance, related to the heat equation.

 

The number of differential equations that have received a name, in various scientific areas is a witness of the importance of the topic. See List of named differential equations.

== Ծանոթագրություններ ==

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