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Difference between small delta t, big delta t, and dt? 
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#1
Aug212, 02:39 AM

P: 53

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.



#2
Aug212, 08:11 AM

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PF Gold
P: 39,348

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.



#3
Aug212, 08:46 AM

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PF Gold
P: 12,016

The last symbolism has a rather wellestablished meaning from the calculus of variations, but as HallsofIvy said, this is by no means a dominantborderingonuniversal meaning.



#4
Aug212, 09:42 PM

P: 53

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 hbar. 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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