Julia Thompson wrote:
>
> Jan Coffey wrote:
> >
> > --- Doug Pensinger <[EMAIL PROTECTED]> wrote:
> >
> > > But you have to memorize math too - you don't just figure things out
> > > every time you do a problem do you?
> >
> > Actualy yes, I do.
>
> OK, 2-part question:
>
> 1) Did you take Differential Equations?
>
> 2) If so, derive the Heat Equation. >:)
Sure. Heat behaves like a fluid, where the amount of
heat in a given small region is proportional to its temperature,
T. So the rate of change of temperature with time, dT/dt, is
proportional to the net rate of heat flow into the region. By
Newton's Law of Cooling, the rate of heat flow from one small
region to the next is proportional to the temperature difference
between the regions, that is to dT/dx, where x is the direction
from one region to the other. If the small regions are lined up
along the x-axis, the heat flow into a region is then
proportional to dT/dx at the right side of the region minus dT/dx
at the left side. But this is essentially the second derivative,
d^2 T / dx^2. This gives the one-dimensional heat equation:
dT/dt = k * d^2 T / dx^2, where k is the constant of proportionality
(Actually, every 'd' is a 'del'.) (To go to more dimensions,
just add the contributions for each, giving
dT/dt = k * (d^2 T / dx^2 + d^2 T / dy^2), etc.)
Does that count? : )
The one class where I ever snuck in a cheat sheet of
formulas was Thermodynamics, though. So I get your point! It's
not so much a matter of not being able to derive things, as a
matter of just not having sufficient time to do so.
---David
Who somehow did memorize the quadratic formula...
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