What Does the Symbol in the Heat Equation Represent?

[superaznnerd]

what does the symbol before the first "u" on the left side of the equation mean?



It is found on this wiki page under the section "derivation in one dimension"

http://en.wikipedia.org/wiki/Heat_equation

the wiki page kind of just skipped a step, and didnt explain what the symbol meant

Thakns!

 

[alxm]

$$\partial$$? Indicates a partial derivative.

I'm not sure I'd say they're skipping a step. The heat equation is a partial differential equation.
It wouldn't make sense to try to explain it without assuming a knowledge of partial differentiation first. You have to study multivariate calculus before you can study PDEs.

 

[Rasalhague]

http://en.wikipedia.org/wiki/Partial_derivative

The partial derivative

$$\frac{\partial u}{\partial t}$$

is the derivative of u with respect to t while holding constant any other variables that u depends on. The Khan Academy has two short videos introducing the idea, "Partial Derivatives" and "Partial Derivatives 2", in the Calculus playlist here:

http://www.khanacademy.org/