Stokes' theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls or simply the curl theorem, is a theorem in vector calculus on
The line integral of … See more

The proof of the theorem consists of 4 steps. We assume Green's theorem, so what is of concern is how to boil down the three-dimensional complicated problem (Stokes' theorem) to a two-dimensional rudimentary problem (Green's theorem). When proving this … See more

Let $${\displaystyle \Sigma }$$ be a smooth oriented surface in $${\displaystyle \mathbb {R} ^{3}}$$ with boundary $${\displaystyle \partial \Sigma \equiv \Gamma }$$. … See more

Irrotational fields
In this section, we will discuss the irrotational field (lamellar vector field) based on Stokes' … See more