-3

I know that:

1) Change in $x$ ie., $Δx$, when $\lim Δx→0$, then $Δx$ is replaced by $dx$.

2) I also know that $∂x$ is used in partial derivative.

Then what is $δx$? Is $dx$ and $δx$ is just the same or something different. I want some mathematical explanation.

Qmechanic
  • 201,751
Roshan Leyangi
  • 93
  • 1
    It all depends on the context. As much as we want to believe, there is not a universal mathematical notation for certain things. Please give the context as to where this occurs so others can answer the question in the best way possible. – BioPhysicist Sep 05 '18 at 13:28
  • As Aaron said, it really depends on the context, but I have seen many times δx just as a fancy way to write dx (yes, they are the same, which I think is your doubt). – user190081 Sep 05 '18 at 13:35
  • 2
    It depends, but one widespread usage of the $\delta$ convention is in calculus of variations problems. – Avantgarde Sep 05 '18 at 13:38
  • Is it really that dx and δx is just the same and nothing more? – Roshan Leyangi Sep 05 '18 at 13:45
  • Every book has its own nomenclature, so you should see that for your purpose. For example, Cengel uses δx for showing inexact differentials. – Shah M Hasan Sep 05 '18 at 13:48
  • 1
    It would be easier if you provide an example, a formula where you have seen this notation and you are not sure about the meaning. I would be temped to say that dx and δx are the same things most of the cases, but you also have functions like the Kronecker delta which use that symbol. – user190081 Sep 05 '18 at 13:50
  • @RoshanLeyangi They can be the same, or they cannot be the same. It all depends on the context. Please supply that context so we can answer the question. – BioPhysicist Sep 05 '18 at 13:57
  • @AaronStevens Do you have any example. – Roshan Leyangi Sep 05 '18 at 14:02
  • To what specific person does the pronoun "he" refer? – WillO Sep 05 '18 at 14:04
  • 2
    Possible duplicates: https://physics.stackexchange.com/q/65724/2451 and links therein. – Qmechanic Sep 05 '18 at 14:12
  • 2
    See also https://physics.stackexchange.com/q/153791/25301 – Kyle Kanos Sep 05 '18 at 14:16
  • 1
    @RoshanLeyangi My examples don't matter. The context you are using does. – BioPhysicist Sep 05 '18 at 14:36

1 Answers1

1

Generally, I've seen "$\delta x$" to mean a tiny change in $x$, without necessarily invoking all of the mathematical machinery of a derivative. In a derivation, you might start with variables $ \delta x $ and $\delta t$ as ordinary quantities, and then later put in an explicit step that takes the limits as they approach $0$.

Tetra
  • 456