Lower case delta or just a regular d?

[beezey]

When integrating and differentiating I'm not sure weather to use a lower case delta or just a d. Is there a time when one is more a appropriate then another or does it not even make a difference? Are they to completely different things? I know it might seem trivial but I have no idea which is right. Help me please.

 

[Stainsor]

Lower case delta is reserved for small but measurable ("finite") changes in some quantity. The d symbol is used in it's place when the change in that quantity is so small that it approaches zero ("infinitesimal").

When integrating and differentiating you should just use a d.

In fact the whole idea behind integrals and derivatives is that you take the limit as the change in your variable approaches zero.

For example, for a derivative you're taking the value of a function (y=f(x)) at two different points that are extremely close together. Then you find the slope by dividing the change in the function or "rise" (in this case dy) and divide it by the change in your variable or "run" (in this case dx). So the derivative of y is dy/dx.

 

[lapo3399]

edit: Should've checked before posting :$.

 

[Gib Z]

Umm actually I think Stainsor got it quite wrong.

The lower case delta is reserved to denote the PARTIAL derivative of a function. Partial derivatives are used when the function has more than 1 variable eg f(z)=xy. We can't just say the derivative of, we must say the derivative of with respect to x or y. For single variable calculus, or regular diffentiation, which is what you want, its just a normal d.

 

[Hurkyl]

The symbol for partial derivatives isn't a delta (\delta) -- Wikipedia reports that it's a rounded variant of the letter d.

 

[Gib Z]

Yea I just realized that after I posted that in a hurry, I had to leave >.< My apologies, Stainsor is right on the money.