What would you choose as the Top 5 Equations? Top 10?
Equations are of central importance in all of science and engineering, but especially so in 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:
(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?
PS: Also posted today in the Computational Scientists & Engineers group at LinkedIn, and also will post soon at my personal blog.