The difference between δt and dt?
When written in an equation, what is the difference between δu and du? (or δt and dt)
Currently viewing it in a fluid mechanics book, but i cant work out what the difference is.
Update:Yeah, its what supposed to be (delta)t.
But, i cant say i've come across partial differentials before, how are they used in calculation.
If it helps, its viscosity im looking at just now.
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δt => an inexact differential
dt => an exact differential
An inexact differential is a mathematical quantity used to
denote a function that is not a state function of the system
and are thus path dependent; like work and heat.
The process involved in reaching the final state must
be accounted for.
An integrating factor must be found to be able to integrate
the function.
An inexact differential cannot be expressed as a total
differential.
On the other hand, an exact differential is path independent
and is applicable to all state functions
An exact differential is a total differential.
Hth
Ah fluid mechanics, love that stuff. If you say its the partial differential version of (delta)t then don't panic. A partial differential is really very simple, it's just a little strange perhaps at first viewing. Imagine you had an equation like this
y=2xt
Lets assume d is the partial differential- the curly d in the previous answer, sorry can't find the symbol on my computer.
To find dy/dx you would assume ALL OTHER VARIABLES ARE CONSTANT so, although t is a variable in this equation we now assume it is constant. So dy/dx=2t.
The same for dy/dt ---> x is now constant so dy/dt=2x
Have a read of this http://en.wikipedia.org/wiki/Partial_derivative if it's still not making any sense. Alternatively try looking in any higher level maths textbook (university level).
And enjoy your viscosity :-)
Essentially, there is no difference. Both are used to indicate a small change. I think, if anything, the "dt" always means an infinitesimal whereas the other form allows for small but not necessarily infinitesimal. Although I have seen both symbols used interchangeably.
Δδ (Delta)
Δ represents:
a finite difference
a difference operator
the Laplace operator
the angle that subtends the arc of a circular curve in surveying
the Determinant of an inverse Matrix (mathematics)
the maximum degree of any vertex in a given graph
the difference or change in a given variable, e.g. ∆v means a difference or change in velocity
distance to Earth, measured in astronomical units
Heat in a chemical formula
http://en.wikipedia.org/wiki/Greek_letters_used_in...
If you mean ∂t, then it is a partial differential. When dt is total differential.