Is the symbol dx equivalent to Δx in these situations?

[karkas]

I have seen the symbol dx in differential equations, but recently I saw it appear in various other equations that I previously thought included Δx instead of dx.

Are those two symbols the same? I mean, is Δx = dx = x_final - x_initial ?

This may be the wrong thread, but I am still a newcomer, and plus I thought I saw another such question around here before!

Thanks

 

[tiny-tim]

Welcome to PF!

I have seen the symbol dx in differential equations, but recently I saw it appear in various other equations that I previously thought included Δx instead of dx.

Are those two symbols the same? I mean, is Δx = dx = x_final - x_initial ?

Hi karkas! Welcome to PF!

∆x is an actual difference.

dx is an infinitesimal difference.

dx/dt = lim{∆x(t)/∆t} = lim{[x(t+∆t) - x(t)]/∆t}.

(for linear functions, of course, it makes no difference)

So Δx = x_final - x_initial is correct

but dx = x_final - x_initial is wrong

 

[karkas]

Thanks Tiny - tim!

Yet I still don't understand something (probably it's because we're taught everything in Greek and I am still not adept with English terminology).

If I say that the speed is v = Δx/Δt and v = dx/dt is the same thing if there is no force disrupting the linear movement?

 

[tiny-tim]

Thanks Tiny - tim!

Yet I still don't understand something (probably it's because we're taught everything in Greek and I am still not adept with English terminology).

If I say that the speed is v = Δx/Δt and v = dx/dt is the same thing if there is no force disrupting the linear movement?

hmm … mathematical symbols should be an international language!

Yes, v = dx/dt is always correct …

but if there's no acceleration, then v = ∆x/∆t is also correct.

However, when you write dx/dt, you don't need to explain it,

but when you write ∆x/∆t, you need to specify a particular interval.

 

[Dr.D]

In physics and engineering, cap delta is frequently used to denote a finite change, a little bit of something. Thus cap delta x denotes a finite change in x.

It is common in setting up a problem to write things in terms of finite differences before passing to the limit when these differences, in the form of ratios, become derivatives.