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1-forms

Name: Anonymous 2008-04-02 22:38

Can anyone give me a somewhat simplistic explanation of 1-forms?  For some reason I'm really stuck on this, I understand that they're a linear transformation mapping point and a vector to R.  (I'm guessing they actually map to all of C but for sake of learning I'd appreciate it simplified as my understanding of complex analysis is virtually nonexistant at this point in time.)  I don't even understand their purpose, except that a differential is a type of 1-form.  The wikipedia article was a bit over my head & the wolfram article wasn't much help either.

Name: Anonymous 2008-04-09 2:41

>>5
note dx1 = df1/dx1 + df2/dx1 + ... + dfn/dx
where the d's on the left hand side should be partial derivatives not normal derivatives

the 1 form defined as such takes a vector function (at a point) to the reals. if you don't have a point, it just gives a real valued function. it is linear because differentiation is linear.

you really should take geometry or advanced calc to understand this properly

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