What do these mean pdv . vdp . d(pv)? I am a bit new to calculus and if we have two variables p and v
$$pdv \ vdp \ d(pv)$$
what will the above quantities representmean ?
 A: You can think of it as the relation of the changes between two quantities as we put some 'perturbation' into the system. It is more transparent for finite changes:
$$ \Delta (PV) = V \Delta P + P \Delta V + \Delta P \Delta V$$
Now, suppose we make the magnitude of changes very small $ \Delta P , \Delta V \to (0,0)$ then:
$$ d(PV) = V dP + P dV$$
This is useful for relating the 'change' in thermodynamic variables.

Illustration
Suppose we are dealing with an ideal gas and $PV= nRT$ , assuming constant moles :
$$ nR dT = V dP + PdV$$
Suppose we have a reversible isothermal process, then $ dT = 0$,
$$ V dP = - P dV$$
Or,
$$ \frac{-V}{P} = \frac{dV}{dP}$$
Since volume is always greater than zero and pressure is greater than zero, it is easy to see as we increase the volume $ \frac{-V}{P}$ becomes more negative, so the decrease in volume as we increase pressure more and more is much greater. Indeed, we have found the partial derivative of volume with pressure at constant temperature:
$$ \frac{-V}{P} = (\frac{\partial V}{\partial P})_T$$
tl;dr: the relation between 'small changes' in a system, helps us understand how the system behaves to be given 'small disturbances'. eg: I give a small disturbance in pressure, then how does my volume change if the process is reversible isothermal?
Edit: Oops! flipped the fraction by accident.
