Vector Integral Calculus: Feynman's Physics Explained
Differential laws describe what happens at each point; integral laws describe the overall behavior. Gauss's theorem says the total flux of a field flowing out of a closed surface equals the sum of all the little sources (the divergence) inside it. Stokes' theorem is the partner statement: the total circulation around a closed loop equals the sum of all the little swirls (the curl) on the surface it encloses.
The big idea
What flows out of a surface equals the sources packed inside it.
Think about it
If you know how much water leaves a closed bag's surface, what does that tell you about taps or drains hidden inside?
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