This article is about the concept from elementary differential calculus. For the generalized advanced mathematical concept from differential topology and differential geometry, see closed and exact differential forms.
In multivariate calculus, a differential or differential form is said to be exact or perfect (exact differential), as contrasted with an inexact differential, if it is equal to the general differential for some differentiable function in an orthogonal coordinate system (hence is a multivariable function whose variables are independent, as they are always expected to be when treated in multivariable calculus).
An exact differential is sometimes also called a total differential, or a full differential, or, in the study of differential geometry, it is termed an exact form.
The integral of an exact differential over any integral path is path-independent, and this fact is used to identify state functions in thermodynamics.
and 29 Related for: Exact differential information
calculus, a differential or differential form is said to be exact or perfect (exactdifferential), as contrasted with an inexact differential, if it is...
In mathematics, an exactdifferential equation or total differential equation is a certain kind of ordinary differential equation which is widely used...
and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0), and an exact form is a differential form...
of differential form. In contrast, an integral of an exactdifferential is always path independent since the integral acts to invert the differential operator...
through by an integrating factor allows an inexact differential to be made into an exactdifferential (which can then be integrated to give a scalar field)...
In mathematics, the term exact equation can refer either of the following: Exactdifferential equation Exactdifferential form This disambiguation page...
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other...
theory based on the existence of differential forms with prescribed properties. On any smooth manifold, every exact form is closed, but the converse may...
The differential, or infinitesimal increment, for the internal energy in an infinitesimal process is an exactdifferential dU. The symbol for exact differentials...
independent book publishing company Exact Editions, a content management platform Exactdifferentials, in multivariate calculus Exact algorithms, in computer science...
In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different...
geometry. Closed and exactdifferential forms Complex differential form Vector-valued differential form Equivariant differential form Calculus on Manifolds...
N_{s}\rangle \mu _{s}+ST.} Exactdifferential: From the above expressions, it can be seen that the function Ω has the exactdifferential d Ω = − S d T − ⟨ N...
same, then the integral of an inexact differential may or may not be zero, but the integral of an exactdifferential is always zero. The path taken by a...
In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function...
nonlinear differential equations with known exact solutions. A notable special case of the Bernoulli equation is the logistic differential equation. When...
which is written dY. The quantity dY is an exactdifferential, while δX is not, it is an inexact differential. Infinitesimal changes in a process function...
In order to solve the equation, we need to transform it into an exactdifferential equation. In order to do that, we need to find an integrating factor...
methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs)....
A differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written...
=\nabla {\varphi }\cdot d\mathbf {r} } in the line integral is an exactdifferential for an orthogonal coordinate system (e.g., Cartesian, cylindrical...
an exactdifferential. In other words, the integral of dΦ will be equal to Φ(t1) − Φ(t0). The symbol δ will be reserved for an inexact differential, which...
list of real analysis topics, list of calculus topics. Closed and exactdifferential forms Contact (mathematics) Contour integral Contour line Critical...
the amount of work done over a cyclic process as: Since dU is an exactdifferential, its integral over any closed loop is zero and it follows that the...
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...
needed] partial differential equations. In general, this makes them hard to solve. Nonetheless, several effective techniques for obtaining exact solutions have...
Global Information
