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Differential equations are an important area of mathematical analysis with many applications in science and engineering. Analysis is the branch of mathematics dealing with continuous functions , limits , and related theories, such as differentiation , integration , measure , infinite sequences , series , and analytic functions .
The term differential is used nonrigorously in calculus to refer to an infinitesimal ("infinitely small") change in some varying quantity. For example, if x is a variable, then a change in the value of x is often denoted Δx (pronounced delta x). The differential dx represents an infinitely small change in the variable x. The idea of an ...
Following twentieth-century developments in mathematical analysis and differential geometry, it became clear that the notion of the differential of a function could be extended in a variety of ways. In real analysis , it is more desirable to deal directly with the differential as the principal part of the increment of a function.
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. [1] In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.
In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. [1] ... functional analysis, differential geometry, ...
In numerical analysis, numerical differentiation algorithms estimate the derivative of a mathematical function or function ... Differential quadrature is the ...
In mathematics education, calculus is an abbreviation of both infinitesimal calculus and integral calculus, which denotes courses of elementary mathematical analysis.. In Latin, the word calculus means “small pebble”, (the diminutive of calx, meaning "stone"), a meaning which still persists in medicine.
The following notation will be used throughout this article: is a fixed positive integer and is a fixed non-empty open subset of Euclidean space. = {,,, …} denotes the natural numbers.