Stokes and Gauss

[where_was_i]

So I was reading about Stoke's and Gauss's laws, and I was curious if there are analogous laws for other dimensions. For example, can you jump from a four dimensional integral to a five dimensional integral by using the proper combinations of curls and gradients? Most of my experience with vector calculus has been for more mundane things like

Comments

[samtaburetkin]

If anything, people want to reduce dimensions, not increase them. And generally there are no flows/vector fields neither in statistics nor in economics (don't know about quantum mechanics though), so it won't be that terribly useful in those fields.

[joshua_green]

Yes you can, and it even extends to integration over manifolds.  The extended version is still known as Stokes' Theorem and includes the versions you're familiar with.

[somnambulat0rz]

Yeah, the generalized Fundamental Theorem of Calculus.