Understanding Δx: The Meaning and Importance of Uppercase Delta in Math

[MarcAlexander]

So I'm aware that the triangle is uppercase delta which means the difference between: 10$\Delta$5=5

But what does Δx mean?

 

[DrGreg]

It means the difference between two values of the variable x, between two specified events.

 

[noxxo]

It means the change in x. For x(at event 1) = 2 and x(at event 2) = 4 : delta x = 4-2 = 2

 

[nonequilibrium]

sometimes it is also used to refer to uncertainty in the variable x
what kind of "uncertainty" depends on the context: experimental, or pertaining to it being defined, ...

 

[brocks]

So I'm aware that the triangle is uppercase delta which means the difference between: 10$\Delta$5=5

Actually I've never seen that use of it. I'm not saying it's wrong, but it's unusual.

But in elementary math texts, $\Delta$x means the amount of change in the variable x. For example, the slope of a line is $\Delta$y/$\Delta$x, i.e. the change in y divided by the change in x, for any two points on the line.

When you learn calculus, you will see that the instantaneous velocity of an object traveling along the x-axis is the limit of the displacement divided by the elapsed time, $\Delta$x/$\Delta$t, as $\Delta$t approaches zero.

 

[Allenman]

It's already been answered pretty good. But just to clarify:

$\Delta$x = x$_{2}$-x$_{1}$

or the slope of a function:
$\frac{\Delta y}{\Delta x}$ = $\frac{y_{2} -y_{1}}{x_{2}-x_{1}}$

Which you'll find to be very similar to the definition of a derivative in calculus:
$\frac{\delta y}{\delta x}$ which basically means (difference in y)/(difference in x)

Capital delta is looking for a specific answer (most times) while lower case is looking for another equation (most times).

 

[MarcAlexander]

It's already been answered pretty good. But just to clarify:

$\Delta$x = x$_{2}$-x$_{1}$

or the slope of a function:
$\frac{\Delta y}{\Delta x}$ = $\frac{y_{2} -y_{1}}{x_{2}-x_{1}}$

Which you'll find to be very similar to the definition of a derivative in calculus:
$\frac{\delta y}{\delta x}$ which basically means (difference in y)/(difference in x)

Capital delta is looking for a specific answer (most times) while lower case is looking for another equation (most times).

What book would provide me with a quick reference to the use of greek letters in Physics?

 

[Pythagorean]

Most symbols have different meanings in different contexts. Pi is one of the few symbols that has a consistent meaning.

 

[Allenman]

What book would provide me with a quick reference to the use of greek letters in Physics?

this is helpful:
http://www.dpi.state.nc.us/docs/accountability/testing/eoc/Physics/physicsreferencetable.pdf

This has all the Greek symbols:
http://en.wikibooks.org/wiki/Physics_Study_Guide/Greek_alphabet