What would you choose as the Top 5 Equations? Top 10?

I was going to write my thoughts on the issue of “Universe: Finite or Infinite?” this weekend. Though the weekend has technically already begun, I have been busy at my day-job. Further, though I have been hurriedly jotting down my points in a small pocket notebook (a habit that has come to serve me well), I still have not found the time to put them in a computer file (usually, just a .txt file) and order them. I hope to be doing the upcoming week. However, in the meanwhile, the title question struck me, and so, I decided to “ship it out” this blog post. Read, and do let me know your thoughts…

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Equations are of central importance in all of science and engineering, but especially so in physics and mechanics.

Even leaving aside algebraic equations, handbooks on PDEs alone list hundreds of equations. However, a few of these do stand out, either because they encapsulate some fundamental aspect of physics/science/engg., or because they serve as simpler prototypes for more complex situtations, or simply because they are so complex as to be fascinating by themselves. There might be other considerations too… But the fact is, some equations really do stand out as compared to others.

If so, what equations would you single out as being most important or interesting? To make the matters more interesting, first, please think of making a short list of only 5 equations. Then, if necessary, make it one of 10 equations—but no more, please! 🙂

As to me, here is my list, put together in a completely off-hand manner:

Top five:
(1-3) The linear wave-, diffusion- and potential-equations.
(4) The Schrodinger equation
(5) The Navier-Stokes equation

Additionally, perhaps, these equations:
(6) The Maxwell Equations
(7) The equation defining the Fourier transform
(8) Newton’s second law (dp/dt = F)
(9) The Lame equation (of elasticity)

Am I already nearing the limit or what… Hmm… But, nope, I am not sure whether I want to include E = mc^2. … I will give this entire matter a second thought some time later on.

But, how about you? What would be your choices for the top 5/10 equations? Why?

(Also posted today in the Computational Scientists & Engineers group at LinkedIn, and at iMechanica [^]).

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A Song I Like:
(Hindi) “wahaan kaun he teraa…”
Singer and Music: S. D. Burman
Lyrics: Shailendra

[PS: Song was “TBD” while publishing this post yesterday. Added the song on May 1, 2011. … Still, I am not sure if I haven’t mentioned this song before. I will check later on, and if so, will replace it with some other song.]

[E&OE]

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