The following conditions are equivalent for a conservative vector field:
- 1. For any oriented simple closed curve C, the line integral
.
- 2. For any two oriented simple curves
and
with the same endpoints,
.
- 3. There exists a scalar potential
function f such that
where,
is the gradient.
- 4. The curl
.
Curl, Gradient, Line Integral,
Poincaré's
Theorem, Potential
Function, Vector Field
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Eric W. Weisstein. "Conservative Field." From MathWorld--A Wolfram Web
Resource. http://mathworld.wolfram.com/ConservativeField.html
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