I am trying to understand how the below listen mathematical theorems and functions are related to each other but the informations regarding this are scrabbled all over and it's getting confusing. The four major theorems at the culmination of multivariable calculus:
- Green's theorem
- 2D divergence theorem
- Stokes' theorem
- 3D Divergence theorem
Now I know:
Green's theorem is a 2D special case of Stokes' theorem, or said in another way Stokes' theorem is the 3d version of Green's theorem (I assume the sentences mean the same thing). (And the Stokes' theorem is a special case of the generalized stokes theorem regarding manifolds).
Now on Wikipedia this is what it is written regarding the Green's Theorem and the 2D divergence theorem:
"Considering only two-dimensional vector fields, Green's theorem is equivalent to the two-dimensional version of the divergence theorem"
Does this mean that the 2D case of the Stokes' theorem is nothing more than the 2D case of the divergence theorem?
Basically I'd like to know how each of the 4 mentioned theorems are related to each other!