Transcription of Introduction to di erential forms
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Introduction to di erential forms
Introduction to differential formsDonu ArapuraMay 6, 2016 The calculus of differential forms give an alternative to vector calculus whichis ultimately simpler and more flexible. Unfortunately it is rarely encounteredat the undergraduate level. However, the last few times I taught undergraduateadvanced calculus I decided I would do it this way. So I wrote up this briefsupplement which explains how to work with them, and what they are good for,but the approach is kept informal. In particular, multlinear algebra is kept toa minimum, and I don t define manifolds or anything like that. By the time Igot to this topic, I had covered a certain amount of standard material, which isbriefly summarized at the end of these thanks to Jo ao Carvalho, John Crow, Mat u s Goljer and Josh Hill forcatching some 1- forms .
1.3 Parametric curves Before discussing line integrals, we have to say a few words about parametric curves. A parametric curve in the plane is vector valued function C: [a;b] !R2. In other words, we let xand ydepend on some parameter trunning from ato
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