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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.

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

My textbook states the following:

$$Wnet=Wnon−conservative+Wconservative$$ $$Wnon−conservative=ΔKE+ΔPE$$ $$Wconservative=−ΔPE$$ $$Wnet=ΔKE$$

$$W=FDcos(Θ)$$

However, my teacher states that $$W=ΔE=ΔUg+ΔUspring+ΔKE+ΔEthermal$$

I understand how the textbook derived it's equations but I'm failing to see how exactly my teacher came up with his equation.

Any help is greatly appreciated.

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.