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[Tellemurius]

I'd probably go for the theory of thermodynamics:
dU = dQ + ΣdW_ⁱ
TdS = dQ
pdV = dW_pr
Σμdx = dW_chem
PV/RT = Z           (You can actually derive this one, but it was first determined experimentally. Besides that you'll need a bit of quantum mechanics or you end up with a wrong factor)

Should be enough for most applications (though you may need a few extra W-terms if you're working with sources of energy besides heat, pressure and chemical). Most other thermodynamical properties can be derived from this small set of equations.

God that was the simplest theories ever to be created.

[Vector]

Actually, I'm quite fond of Newton's laws of motions.  I love mechanics.

Too bad physics isn't interested in that stuff anymore =/

[Leafsnail]

God that was the simplest theories ever to be created.

And yet it has such profound implications...

Actually, I'm quite fond of Newton's laws of motions.  I love mechanics.

Too bad physics isn't interested in that stuff anymore =/

There isn't that much more to do on Newtonian mechanics itself, I guess.  The ideas have been refined by relativity and the like, though, which are still being explored in more depth.

[Nadaka]

Call me weird, but I like the ideal gas law. pV = nRT.

[Dr. D]

I think that Newton's laws will be much more fun for me next semester, when I finally get to solve some differential equations to see how things move.

The first day in my high school chemistry class the teacher showed us some rap some people had made with the ideal gas law. Unfortunately for her, she did not notice the cursing in the video.

[Nadaka]

The part about Newtonian motion that I don't like is that its a pain to solve for the position of a body in an elliptical orbit given orbital parameters, an initial position and delta T. I ended up resorting to an iterative approximation.

[Virex]

I'd probably go for the theory of thermodynamics:
dU = dQ + ΣdW_ⁱ
TdS = dQ
pdV = dW_pr
Σμdx = dW_chem
PV/RT = Z           (You can actually derive this one, but it was first determined experimentally. Besides that you'll need a bit of quantum mechanics or you end up with a wrong factor)

Should be enough for most applications (though you may need a few extra W-terms if you're working with sources of energy besides heat, pressure and chemical). Most other thermodynamical properties can be derived from this small set of equations.

God that was the simplest theories ever to be created.

Was it? I was under the impression that it took almost a whole century before the equations as we now know them came to be. Plus the base is simple but it can be a complete headache in some cases (so much even that the method that in theory should be able to describe the thermodynamic quantities of liquids and non-ideal gases (using virial coefficients) isn't usable because we can't get a grip on the equations needed to take higher-order interactions between particles into account)

[Osmosis Jones]

I think that Newton's laws will be much more fun for me next semester, when I finally get to solve some differential equations to see how things move.

Yes and no. Absolutely everything seems to come down to 2nd order differential equations. It's nifty at first, but it does get old fast. That said, have you learnt how to solve the Lagrangian of a system yet? (Solving a system as a function of its energy rather than component forces).

[Grek]

Bayes Theorem!

P(b)*P(a|b)=P(b|a)*P(a)