I was reading lethe's thread on differential forms and suddenly it dawned on me that I had no idea what differential forms were for, or why the process was developed. Do they replace vector calculus, or are they a more powerful form of linear algebra or what? For me it is much easier to study something if I know why I'm studying it, and what the benefits are. Any enlightenment would be greatly appreciated. BTW I'm just an interested layperson who studies physics simply because I find it fascinating.