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

[schrodingerscat11]

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, "$\Delta x$" 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). "$\delta x$" 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.

 

[schrodingerscat11]

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.