My textbook states the following:
$$W_{net}=W_{non−conservative}+W_{conservative}$$ $$W_{non−conservative}=ΔKE+ΔPE$$ $$W_{conservative}=−ΔPE$$ $$W_{net}=ΔKE$$
$$W=FDcos(Θ)$$
However, my teacher states that $$W=ΔE=ΔUg+ΔU_{spring}+ΔKE+ΔE_{thermal}$$
Which I think can be rewritten as: $$W=ΔPE+ΔKE+ΔE_{thermal}$$
But I'm at a loss for where to go from here.
I understand how the textbook derived it's equations but I'm failing to see how exactly my teacher came up with $W=\Delta E$
Any help is greatly appreciated.
Edit: For reference, I'm using the OpenStax textbook. The summary for the section I'm referencing can be found here: https://openstax.org/books/college-physics-ap-courses-2e/pages/7-section-summary