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Examples of path functions include work, heat and arc length. In contrast to path functions, state functions are independent of the path taken. Thermodynamic state variables are point functions, differing from path functions. For a given state, considered as a point, there is a definite value for each state variable and state function.
In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a system) that depend only on the current equilibrium thermodynamic state of the system [1] (e.g. gas, liquid, solid, crystal, or emulsion), not the path which ...
However, different paths can trace the same set of points. In mathematics, a path in a topological space is a continuous function from a closed interval into . Paths play an important role in the fields of topology and mathematical analysis. For example, a topological space for which there exists a path connecting any two points is said to be ...
For including parser functions, variables and behavior switches, see Help:Magic words; For a guide to displaying mathematical equations and formulas, see Help:Displaying a formula; For a guide to editing, see Wikipedia:Contributing to Wikipedia; For an overview of commonly used style guidelines, see Wikipedia:Simplified Manual of Style
Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
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 ...
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Shortest path (A, C, E, D, F), blue, 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.