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

In summary, the conversation is about the difference between Δf, δf, and df, and their meanings in terms of changes in a function. The speaker is studying solid state physics and is confused by the notations used in the equations of motion. Another person explains that Δf represents a specific change in the function, while df is the differential as defined in Calculus. δf can have various meanings and should be defined in context. The speaker also asks about the change in symbols from δk to dk and δt to dt, which are not necessarily the same.
  • #1
schrodingerscat11
89
1
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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  • #2
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
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.
 
  • #4
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.
 

1. What is the difference between small delta t and big delta t?

The terms "small delta t" and "big delta t" refer to the size or magnitude of the time interval being measured. Small delta t refers to a short or small time interval, while big delta t refers to a longer or larger time interval.

2. How are small delta t and big delta t related to each other?

Small delta t and big delta t are inversely related, meaning that as one increases, the other decreases. This is because delta t represents a change in time, and as the change gets larger, the time interval being measured gets smaller.

3. What is dt in relation to small delta t and big delta t?

dt is a common notation used to represent a small change in time, similar to small delta t. It is often used in mathematical equations to represent a small or infinitesimal time interval. Therefore, dt is related to both small delta t and big delta t, as it is used to measure changes in time regardless of the interval size.

4. How is delta t different from dt?

Delta t and dt are often used interchangeably, but there is a subtle difference between them. Delta t represents a specific time interval or duration, while dt represents a small or infinitesimal change in time. In other words, delta t is a specific value, while dt is a notation used to represent a small change in time.

5. Why are small delta t and big delta t important in scientific research?

Small delta t and big delta t are important in scientific research because they allow for precise measurements of time intervals. By using smaller or larger time intervals, scientists can gather more accurate data and make more accurate predictions. Additionally, small delta t and big delta t are often used in mathematical calculations to model complex systems, making them essential in many areas of scientific research.

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