In calculus, the differential represents the principal part of the change in a function y = f ( x ) {\displaystyle y=f(x)} with respect to changes in the...

consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations...

mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first...

mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally...

In mathematics, a linear differential equation is a differential equation that is linear in the unknown function and its derivatives, so it can be written...

differences and the derivatives of functions. The term is used in various branches of mathematics such as calculus, differential geometry, algebraic geometry...

differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of...

a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function...

calculus—the study of the area beneath a curve. The primary objects of study in differential calculus are the derivative of a function, related notions...

transcendental constants. A function u of a differential extension F[u] of a differential field F is an elementary function over F if the function u is algebraic...

In a system of differential equations used to describe a time-dependent process, a forcing function is a function that appears in the equations and is...

Boolean variables and Boolean functions. Boolean differential calculus concepts are analogous to those of classical differential calculus, notably studying...

mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified...

unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which...

Gateaux differential of a function may be a nonlinear operator. However, often the definition of the Gateaux differential also requires that it be a continuous...

functions, named after Friedrich Bessel who was the first to systematically study them in 1824, are canonical solutions y(x) of Bessel's differential...

cylinder functions are special functions defined as solutions to the differential equation This equation is found when the technique of separation of variables...

produces a (k+1)-form d φ . {\displaystyle d\varphi .} This operation extends the differential of a function (a function can be considered as a 0-form,...

Differential evolution (DE) is an evolutionary algorithm to optimize a problem by iteratively trying to improve a candidate solution with regard to a...

Biddell Airy (1801–1892). The function Ai(x) and the related function Bi(x), are linearly independent solutions to the differential equation d 2 y d x 2 − x...

mathematics, Mathieu functions, sometimes called angular Mathieu functions, are solutions of Mathieu's differential equation d 2 y d x 2 + ( a − 2 q cos ⁡ (...

integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives...

and differential geometry, such as an infinitesimal change in the value of a function Differential algebra Differential calculus Differential of a function...

antiderivatives. It is also a prototype solution of a differential equation. Differential equations relate an unknown function to its derivatives and are...

converted into a hypergeometric differential equation by a change of variable, and its solutions can be expressed using hypergeometric functions. Since the...

differential equation to be exact. The nomenclature of "exact differential equation" refers to the exact differential of a function. For a function F...

In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its...

A differential is a gear train with three drive shafts that has the property that the rotational speed of one shaft is the average of the speeds of the...

On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree. The...

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow...