Search results
Results from the WOW.Com Content Network
An exact equation may also be presented in the following form: (,) + (,) ′ = where the same constraints on I and J apply for the differential equation to be exact. The nomenclature of "exact differential equation" refers to the exact differential of a function.
In mathematics, the term exact equation can refer either of the following: Exact differential equation; Exact differential form This page was last edited on 28 ...
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 ...
In mathematics, especially vector calculus 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, α, that is the exterior derivative of another differential form β. Thus, an exact form is in the image of d, and a closed form is in the kernel of d.
Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form. If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers.
In general relativity, an exact solution is a (typically closed form) solution of the Einstein field equations whose derivation does not invoke simplifying approximations of the equations, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter.
Gatorade aims to combat the symptoms of dehydration by restoring electrolytes to the body. Naturally, Gatorade’s exact nutritional value will depend on which formula you choose. For instance ...
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.