Confusion about the Work-Energy Theorem

[AznBoi]

Is this expression always true?: $$W=\Delta E$$ Please explain why this is using mathematical computations. I understand it conceptually but I just can't connect the two mathematically.

Also, why does my book only have the expression: $$W= \Delta KE$$ rather than: $$W= \Delta KE + \Delta PE$$ why did they leave the Potential energy out of the expression?

 

[mezarashi]

The equation $$W = \Delta E$$
is simply saying that work done on or by a system causes a change in energy of that system.

As for your textbook, it's hard to say why it left out the potential energy factor, but most likely it is because it has not yet discussed potential energy in that specific section or the potential energy is always assumed to be constant for that particular section.

 

[mathPimpDaddy]

Work is Delta KE

You can look at work as potential.