I've been trying to get a meaningful understanding of the benefits of using differential forms. I've seen examples of physics formulas that are reduced to a very simple declarative form relative to their tensor counterparts. However to me it just seems like a notation change to implied tensor indices. Some texts will say to do any actual computation you need to convert the differential form to tensor notation and work the problem through to completion. Are there some deeper theorems or examples that show the superiority of differential forms over tensor methods? Some of the books I've looked through are Flander's book, Wheeler's Gravitation and Hsu Vector Analysis Outline series book. There's also a series of videos on Youtube most notably by Dave Metzler (others are classroom based tutorials): In Metzler's tutorial he relates the various forms to their vector counterparts which shows some interesting connections between the forms themselves but then what. I'm looking for some example that shows you gain an intuitive understanding of some system by looking at its differential form description.