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- Why are n-forms called differential forms? What is differential about them?

Why are n-forms called

We find in both real calculus and tensor calculus expressions similar to df = f' dx , but it seems to me the quantities in each case are very different things. Aren't they?

*differential*forms? What is differential about them? And why was the dx notation adopted for them? It must have something to do with the differential dx in calculus. But dx in calculus is an infinitesimal quantity. I don't see what n-forms have to do with infinitesimal quantities.We find in both real calculus and tensor calculus expressions similar to df = f' dx , but it seems to me the quantities in each case are very different things. Aren't they?