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...

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

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...

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...

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,...

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

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

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...

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives...

mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The...

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

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

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...

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...

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

represents the order of the Bessel function. Although α {\displaystyle \alpha } and − α {\displaystyle -\alpha } produce the same differential equation, it is...

Differential privacy (DP) is a mathematically rigorous framework for releasing statistical information about datasets while protecting the privacy of...

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...

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...

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

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution...

computation, differential evolution (DE) is a method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure...

is a fundamental tool that quantifies the sensitivity of change of a function's output with respect to its input. The derivative of a function of a single...

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...

differential, if it is equal to the general differential d Q {\displaystyle dQ} for some differentiable function  Q {\displaystyle Q} in an orthogonal coordinate...

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

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

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...

with some ideas of differential calculus and suggested that the "differential coefficient" vanishes at an extremum value of the function. In his astronomical...

In mathematics, a homogeneous function is a function of several variables such that the following holds: If each of the function's arguments is multiplied...