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Stokes' Theorem
★★★★★Graduate+
📖Definition
Stokes' Theorem states the surface integral of curl equals the line integral around the boundary. Generalizes the Fundamental Theorem of Calculus.
📐Formulas
∮_C \vecF · d\vecr = ∬_S (∇ × \vecF) · d\vecS
Stokes' Theorem
∈tₐ^b f'(x)dx = f(b) - f(a)
1D special case (FTC)
✏️Examples
예제 1
Strategy to compute ∮ᴄ F·dr using Stokes?
📜History
Discovered by: George Stokes (1854)
Appeared in Kelvin's letter to Stokes; Stokes used it as exam problem.
⚡Applications
Electromagnetism
Maxwell's equations, Faraday's law
Fluid Dynamics
Circulation, vorticity
Differential Geometry
de Rham cohomology
🔗Related Documents
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