# Green's Theorem History question

1. Dec 9, 2004

### jisland85

I find it a bit interesting that there is a separate theorem for Stokes theorem in a 2D situation. Can someone tell me why this is so? What's the history on these theorems. Did this guy Green come along and generalize Stokes theorem and get credit for it because if this is the case then I will just limit some other theorem to a special case and get my name on it. Silly question I suppose but I was wondering. Thanks . . .

2. Dec 9, 2004

### arildno

From what I know, Green was active around the 1820's, while Gabriel Stokes was about a generation thereafter.

3. Dec 9, 2004

### HallsofIvy

There is a difference between "generalize" and "specialize"!!

What happened was Green proved the theorem in the 2-d (flat) case. Later Stokes proved the more general 3-d theorem.

4. Dec 9, 2004

### jisland85

Ahh, ok, so it was the other way around. Thanks fellows!

5. Dec 9, 2004

### quasar987

For whoever is interested:

We can read in Stewart's Analysis Vol.2 pp.973 (actually we can't cuz I have it in french so it's a rough translation):

"What we call Stokes' theorem was really discovered by Sir William Thompson (Lord Kelvin). Stokes heard of it through a letter from Thompson in 1850 and asked to his students at Cambridge to demonstrate it during an exam (:surprised). We ignore if one of them succeeded."

6. Dec 10, 2004

### Galileo

I've got that book too (but in English). There's a footnote about Green too:

Smart guy, that Green.

7. Dec 10, 2004

### rdt2

from Hestenes, ‘Differential Forms in Geometric Calculus’, 1993.

8. Dec 10, 2004

### fourier jr

isn't the fundamental theorem of calculus a 1-dimensional version of the divergence theorem?

9. Feb 12, 2005

### mathwonk

yes, all the theorems known as grenns, stokes, gauss, divergence, are just higher diemnsional versions of the FTC. The proof reveals this.

just use repeated integration to express the integrand in these theorems as a repeated integral, and the theorem immediately becomes the FTC.

they also appear in the book by maxwell, elctricity and magnetism. to my knowledge most of these accounts of stokes setting the theorem as a prize problem, come from spivak's introduction to his calculus on manifolds.

10. Aug 10, 2008

### tecumseh

Thanks for all this history on Green, Stokes', Maxwell, etc. electro and mag. related.

Gives me greater insight.

Lover of the history of math.

Don Wire