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Differential equations play a prominent role in many scientific areas: mathematics, physics, engineering, chemistry, biology, medicine, economics, etc. This list presents differential equations that have received specific names, area by area.
Differential geometry: General Laguerre: 2 ... List of named differential equations; References This page was last edited on 9 October 2024, at 08:11 (UTC). Text is ...
Properties of the derivative have inspired the introduction and study of many similar objects in algebra and topology; an example is differential algebra. Here, it consists of the derivation of some topics in abstract algebra, such as rings, ideals, field, and so on. [52] The discrete equivalent of differentiation is finite differences.
The order of the differential equation is the highest order of derivative of the unknown function that appears in the differential equation. For example, an equation containing only first-order derivatives is a first-order differential equation, an equation containing the second-order derivative is a second-order differential equation, and so on.
Logarithmic differentiation is a technique which uses logarithms and its differentiation rules to simplify certain expressions before actually applying the derivative. [ citation needed ] Logarithms can be used to remove exponents, convert products into sums, and convert division into subtraction—each of which may lead to a simplified ...
Differential equations are prominent in many scientific areas. Nonlinear ones are of particular interest for their commonality in describing real-world systems and how much more difficult they are to solve compared to linear differential equations.
The exterior derivative of a differential form of degree k (also differential k-form, or just k-form for brevity here) is a differential form of degree k + 1.. If f is a smooth function (a 0-form), then the exterior derivative of f is the differential of f .
In mathematics, geometric calculus extends geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to reproduce other mathematical theories including vector calculus, differential geometry, and differential forms. [1]