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Amsingh123
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How would one prove Stokes' Theorem? I'm 15. I learned about Stokes' Theorem recently and I have a decent understand of it, but I thought that it would be useful to know it's derivation. Thanks for your help, PF.
Stokes' Theorem Proof is a mathematical theorem that relates the surface integral of a vector field over a surface to the line integral of the vector field along the boundary of the surface.
Stokes' Theorem Proof is important because it provides a powerful tool for calculating surface integrals, which are used in many areas of science and engineering such as fluid mechanics, electromagnetism, and differential geometry.
The assumptions of Stokes' Theorem Proof are that the surface is smooth, oriented, and closed, and that the vector field is continuously differentiable.
Stokes' Theorem Proof is closely related to other theorems in vector calculus, such as the Fundamental Theorem of Calculus, Green's Theorem, and the Divergence Theorem. It is a generalization of these theorems to higher dimensions.
Stokes' Theorem Proof has many applications in physics and engineering, including calculating the circulation of a fluid, determining the work done by a force field, and finding the flux of a vector field through a surface.