 
Summary: Introduction to differential forms
Donu Arapura
April 21, 2010
The calculus of differential forms give an alternative to vector calculus which
is ultimately simpler and more flexible. Unfortunately it is rarely encountered
at the undergraduate level. However, the last few times I taught undergraduate
advanced calculus I decided I would do it this way. So I wrote up this brief
supplement which explains how to work with them, and what they are good
for. By the time I got to this topic, I had covered a certain amount of standard
material, which is briefly summarized at the end of these notes.
My thanks to Jo~ao Carvalho and Josh Hill for catching some typos.
Contents
1 1forms 2
2 Exactness in R2
3
3 Parametric curves 3
4 Line integrals 4
5 Work 7
6 Green's theorem for a rectangle 8
7 2forms 8
