Differential and derivatives [HELP]

[xmedium]

Can someone explain to me what are differential and derivatives used for (intergrals ?) in some well known stuff from dynamics or thermodynamics:

dA=Fdr or in thermodynamics PdV

For example what is that dV ... why not just V.

Why do I sometimes write a=d^2r/dt^2 instead of a=r(:)/t(.)

(':' 2nd derivate and '.' is first derivate ------ so sorry for the input I am in a rush)

Thanks.

 

[LostConjugate]

The dots are just a shorthand notation, there is no difference.

dV is a small amount of V. How small? The smallest possible. The exact amount does not need to be known in the context of differential equations.

This is known as "the calculus". There are many notes and courses on the subject.

 

[xmedium]

Im watching now someMIT courses ... is there something similar for this coz I don't really understand what "smallest possible" Work(A) might be :)

 

[LostConjugate]

It might be some multiple of plank's constant. Though it is not important, it's the concept of a limit that is important.

Try starting here: http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

 

[ELog]

Work (A) = Force (F) * Displacement (r)

If the displacement is not a straight line, then we can break the path up into a series of straight lines, and so the work is then the sum of all F*r for each r, or segment of the path. Letting this segment lengths approach zero, the sum becomes an integral and the "r's" becomes "dr's". Differentiating with respect to r, dA/dr = F , or in differential form, dA = Fdr.