What's your favorite equation?

you stole mine!  i love ideal gas law.

i recently used ohm's law at work - i was surprised i even remembered that one.  There was also an entropy relationship I vaguely remember cause I created the pnemonic "you have a great a$$" it wasn't that great because I can't remember the equations now...but that was my fave in college.  

Enzymatic hydrolysis of cellulose.  Chemistry equation (sort of) does that count?

I like the multipurposeness of the convection-diffusion equation.  It works for energy, mass and momentum.  

I like the widely useful minimization of a quadratic cost function. 

I love the wonderful symmetry of Maxwell's equations.  Because of that symmetry, solving them has often led me to that often proven result that 0=0.

I am developing a new affinity for the Euler-Bernoulli beam equation.

I love the wonderful simplifying abstractions possible with matrix algebra.

My relationship with these equations is very personal.  It goes way back in time and down very deep into the darkest recesses of my mind.  They have been both friends and enemies to me.  It has been a lifelong battle to get them to tell me the answer to things I want to know.

I will see if I can figure out a way to get Mathtype to print out an image of each equation (or set of them) to paste in this thread to see if you get the same reaction I do.

In case you cannot tell, I am cleaning out my home office and throwing away boxes and boxes of stuff I've solved.

TW

How do you feel about Boltsman's entropy equation, S=k_B*ln(W)? The ideal gas law is a special case of it.

Boltzman liked it so well himself that it is his epitaph on his gravestone.

TW

This a great mnemonic for whatever it was, (maybe Boltzman).  You need a mnemonic for mnemonic too.

TW

Compound interest.

P = C (1 + r/n) ^nt

Waiting for someone to mention x=n+1 (number of bikes one should own)

I like it just as a picture.  I would have to work on the chemistry to remember what the reactions are.  For a while, I worked on combustion chemistry.  The equations for chemical equilibrium and the related equations for reaction rate are wonderfully simplifying formulas. It still gets very complicated for even the simplest process if you include all the multi-step reactions that are possible.  I liked to just boil it down to a single equivalent step like Arrhenius did.

TW

What is n in your case these days? 

In general, n=n+1 is a discrete time version of the differential equation dn/dt=constant.  in the bike equation, the time variable has been normalized to unity.  To understand your bike situation, I need the time step and the value of n at some point in time. 

TW

Only 6

I modified my post while you were answering.  What is the time step in the equation in years?

Green's Function! How could I forget that one? I have a folder in my hand in which I derived the Green's function for a diffusion equation, (simple enough) and then I showed how it was then in the proper form to use the Euler-Lagrange equation so you could apply the calculus of variations. I used it on the Laplace transform of the time dependent magnetic diffusion equation.  I used calculus of variations to derive the distribution of current for minimum energy consumption for a particular magnetic field distribution as a function of frequency.  I was going to publish it but got stuck trying to up my game to handle the convection diffusion equation which was more useful I thought to fluid flow problems.  Maybe I can do that one.

I should add that the Euler-Lagrange equation is beautiful in and of itself.  And, it comes with a  great story of enormous mathematical ego and it's comeuppance.

me engineer.  me not spell good.

UHGA is something thermodynamic that always equals zero as well...something like U+TdelS=H, H-???=G, G-TdelS=A, A+???=U

Oh yeah, I had to look it up.  Those are the Gibbs-Helmholtz equations.  They are equations relating thermodynamic states. If you know two of the thermodynamic properties of a single material, you can get all other thermodynamic properties of the state.  You can view the following two as defining Gibbs free energy, G, and the Helmholts free energy, A, in terms of internal energy, enthalpy, temperature and entropy. 

G=H-TS,  A=U-TS

There are some more equivalent equations in terms of partial derivatives of the potentials that are hard to type using this editor.

TW

F=ma. Applies to so many things in life.

I like the time-dependent case for Schroedinger's equation too, because it is simple and yet QM was the hardest class I've ever taken.

(schroedinger.png)

I remember struggling with quantum mechanics until I learned that physics just used entirely different symbols for operations than I was used to in math classes.  They abstracted the symbols down to a level that nothing meaningful was left, much as the version of Schroedinger's equation you wrote.  I started writing stuff out in my version of the equations, which were much longer, and I began to understand it.  

Interesting thing, I went into engineering after undergrad.  Since that time, I have never used Schroedinger's equation, not even once.  I haven't even needed to know it even for background.  I use Newton's equation every day.   It says a lot about engineering versus physics.  Of course, I prefer to write it as F=m*(d^2/dt)x.

I have not really had to use any math skills since statistics in undergrad (about 20 years ago), but I use the Pythagorean theorem in real life all the time.

Most recently to figure out how much longer the swim is to the 1st buoy if I started 25 meters wide of the "mess". 

For a 750 meter swim where the 1st buoy is 300 metres away, it turns out its only 1 extra meter.  Sighting of course, is another issue...

I did that one too.  Do you know how much farther you run per lap if you run in the second lane rather than the first on a track?  

Yep that one just hits you like an apple on the head doesn't it?

TW

What do you BTers think about one of the equations from the article?

e^i*pi+1=0

Its got five essential mathematical constants, 0, 1, pi, i, and e; plus it is so improbable.  Sort of cool for that. I am more apt to use the related identity

e^i*x=cos x + i*sin x

TW