Writing on Stoke's, Green's, or Divergence theorem

In summary, for a Calculus III assignment, the teacher wants a 7-page paper on one of the theorems covered in the last chapter of the textbook, including the history and mathematicians behind it. The suggested sources include side notes in the textbook, online research, and the 1854 Smith's Prize exam. One potential source for information on the history of Stokes' theorem is an article by Victor J. Katz in Mathematics Magazine.
  • #1
Bohrok
867
0
I suppose this has to go under homework, so here it goes:
I'm in Calc III and we won't have enough time to cover the last chapter in the textbook about Stokes theorem, Green's theorem, and the divergence theorem, so instead the teacher wants a 7-page paper on something from that chapter. She said we can write about any of the theorems and the mathematicians behind them. She also said we can work out a out problem, but she doesn't want that to be the focus; she's more interested in us writing about the history.

I'm not sure if we can write about more than one theorem (I'll ask her about that soon) but if it turns out she only wants to limit it to one , I don't know how I'll write 7 pages on it :eek: The only useful information I could use is any side notes in the margins of calc textbooks and whatever I can find online. And since I don't know anything about these theorems, I have no idea which one may have more to write about. I'll probably end up skimming the next couple of chapters to get the gist of what these theorems are about and be able to make a more informed decision on what to write about. But until then...

Any suggestions on what theorem has more history and information that could fill up a paper, or any good sources with info on them or the mathematicians?
 
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  • #2
All those theorems are pretty much the same, they are special cases of the general theorem. There is the fact that they are all names after the wrong people. There are applications to physics. There is interesting history. There is the 1854 Smith's Prize exam. It will be easy to reach seven pages and difficult to stop before seventy.

https://www.physicsforums.com/showthread.php?t=115981

you could look at the library for

The History of Stokes' Theorem
Victor J. Katz
Mathematics Magazine
Vol. 52, No. 3 (May, 1979), pp. 146-156
(article consists of 11 pages)
 
  • #3
Thanks for the info and the link to the thread; that'll be a great starting point for the paper :smile:
 

Related to Writing on Stoke's, Green's, or Divergence theorem

1. What is Stoke's, Green's, and Divergence theorem?

Stoke's, Green's, and Divergence theorem are mathematical theorems that relate the surface integral of a vector field to the line integral of the field around its boundary, and the volume integral of a vector field to the surface integral of the normal component of the field over the boundary. They are fundamental concepts in vector calculus and are used to solve many engineering and physics problems.

2. What is the difference between Stoke's, Green's, and Divergence theorem?

Stoke's, Green's, and Divergence theorem are all related to different types of integrals. Stoke's theorem relates a surface integral to a line integral, Green's theorem relates a double integral to a line integral, and Divergence theorem relates a volume integral to a surface integral.

3. How are Stoke's, Green's, and Divergence theorem used in real-world applications?

Stoke's, Green's, and Divergence theorem have many practical applications in fields such as engineering, physics, and fluid mechanics. They are used to calculate flux, work, and other physical quantities in various systems, such as fluid flow, electromagnetic fields, and heat transfer.

4. What are the prerequisites for understanding Stoke's, Green's, and Divergence theorem?

To fully understand Stoke's, Green's, and Divergence theorem, one should have a strong foundation in vector calculus and multivariable calculus. Familiarity with concepts such as vector fields, line integrals, and surface integrals is also necessary.

5. Are there any limitations to Stoke's, Green's, and Divergence theorem?

While Stoke's, Green's, and Divergence theorem are powerful tools for solving problems in vector calculus, they do have limitations. For example, they can only be applied to certain types of vector fields and cannot be used in all situations. Additionally, they may not be applicable to non-continuous or discontinuous functions.

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