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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.
Today's Idaho State Route 78 roughly follows the path of the South Alternate route of the Oregon Trail. In 1869 the Central Pacific established Kelton, Utah as a railhead and the terminus of the western mail was moved from Salt Lake City. The Kelton Road became important as a communication and transportation road to the Boise Basin. [39]
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.
The difference between initial and final states of the system's internal energy does not account for the extent of the energy interactions transpired. Therefore, internal energy is a state function (i.e. exact differential), while heat and work are path functions (i.e. inexact differentials) because integration must account for the path taken.
Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
A three-dimensional hypercube graph showing a Hamiltonian path in red, and a longest induced path in bold black. In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges).
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where k is the wavenumber, and L m and L m − 1 represent the exact path differences. Here the Dirac–Duarte (DD) interferometric equation is a probability distribution that is related to the intensity distribution measured experimentally. [6] The calculations are performed numerically. [5]