I am still Partial to a bit of Calculus

One of the most pervading formulas in all Physics. This is the wave equation.

It is a partial differential equation of the second order.

There are four things that wiggle.

Time, t, and the three spatial coordinates x, y, and z.

So where are they? The formula is in shorthand because it is used so often.

"c" is the speed of the wave.

"u" is the part (made up of "t"'s) that tells us how the wave changes over time. The double dots reminds us that is a second order differential.

Now comes the interesting bit.

The triangle is a capital Greek letter call "nabla".

It is shorthand for the way the wave moves through space. we call it the "del operator" and gives the instructions about how the "u" changes in space.

It is short for





The squiggly "d"'s are there to remind us that this is a partial differential, and the x, y, and z with hats on are telling us which way to point the value of the stuff after them.

This equation is quite general, but has applications wherever waves of any kind are to be found.

The quantum mechanical pearl that is the Shrodinger Equation is just one application.