Difference between small delta t, big delta t, and dt?

physicsjn

Greetings! I am confused with the difference between Δf, δf, and df. I think Δf is a difference between two values, while df and δf refer to infinitesimal change (but I do not know the difference between the two.) Can anybody explain the difference? I am studying solid state physics (I am using Kittel) and the explanation of the equations of motion in semiconductor crystals is confusing without understanding these notations. Thank you very much.

HallsofIvy

Yes, "[itex]\Delta x[/itex]" is the change in f for specific changes in the variables f depends on. "df" is the differential as defined in Calculus. It is, strictly speaking, not an "infinitesal" (which, outside of some very deep logical texts) is at best a loose concept). "[itex]\delta x[/itex]" may have a number of different meanings and should be defined in the text.

arildno

The last symbolism has a rather well-established meaning from the calculus of variations, but as HallsofIvy said, this is by no means a dominant-bordering-on-universal meaning.

physicsjn

Okay. I am kinda confused. How come the differential is not infinitesimal? Isn't it a very small increment to the function? But anyway, I'll just post the transition (from the book) of δt to dt. This is what actually confused me:

δk = -(eE/h)δt
(h)(dk/dt) = -eE

Note: h here actually means h/2*pi or h-bar. I just wrote h to simplify stuff.

Why change the δk to dk and δt and dt? Are the two just the same? Why change symbols all of a sudden? Thanks again.