Calculus › Section P · Vector analysis › Topic P.3

Conservative fields and path independence

Some force fields keep a promise: the work between two points is the same on every route. A potential function is the promise in writing, and a one-line test tells you when to expect it.

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In this topic

The fundamental theorem for line integrals
Path independence and closed loops
Testing for a potential
Worked example: hunting a potential
Worked example: the payoff
Worked example: three variables
The hole in the fine print
Common mistakes to avoid
Key takeaways

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Standards: Beyond AP

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