What is it
Stokes' theorem generalises Green's theorem to three dimensions, relating a line integral around a closed curve to a surface integral of the curl of a vector field over any surface bounded by that curve.
Why it matters
Stokes' theorem underlies Maxwell's equations in electromagnetism, connecting circulating electric and magnetic fields to their sources — making it essential preparation for physics and electrical engineering degrees.
Exam tip
Choosing the simplest possible surface bounded by the given curve (often a flat disc) usually makes the surface integral far easier to calculate — the theorem guarantees any bounded surface gives the same answer, so pick the easiest one.
Related topics
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