Mr. Integral
Math notes/Calculus III/Vector Calculus

Conservative Fields and Potentials — Cheat sheet

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Core rule

F=∇ϕ  ⟹  W=ϕ(B)−ϕ(A).\mathbf F=\nabla\phi\implies W=\phi(B)-\phi(A).

Watch for

Curl zero needs a suitable domain for the converse. Check holes and singularities.