Existence of Potential Functions
In physical applications the functions I and J are usually not only continuous but even continuously differentiable. Schwarz's Theorem then provides us with a necessary criterion for the existence of a potential function. For differential equations defined on simply connected sets the criterion is even sufficient and we get the following theorem:
Given a differential equation of the form (for example, when F has zero slope in the x and y direction at F(x,y) ):
with I and J continuously differentiable on a simply connected and open subset D of R2 then a potential function F exists if and only if
Read more about this topic: Exact Differential Equation
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