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

by physicsjn
Tags: delta, difference
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Aug2-12, 02:39 AM
P: 62
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.
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Aug2-12, 08:11 AM
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PF Gold
P: 39,497
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.
Aug2-12, 08:46 AM
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PF Gold
P: 12,016
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.

Aug2-12, 09:42 PM
P: 62
Difference between small delta t, big delta t, and dt?

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.

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