Inexact differential

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In mathematics, an inexact differential, as contrasted with an exact differential, of a function f is denoted:

[\partial f.] [\int_^ \left (\frac \right) \ne f(b) - f(a)]; as is true of point functions.

An inexact differential is one whose integral is path dependent. This may be expressed mathematically for a function of two variables as [\ If \ df \; = P(x,y) dx \; + Q(x,y) dy,\ then\ \frac \ \ne \ \frac.]

A differential dQ that is not exact is said to be integrable when there is a function 1/τ such that the new differential dQ/τ is exact. The function 1/τ is called the integrating factor, τ being the integrating denominator.

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