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http://planetmath.org/?op=getobj&from=objects&id=4370
that's pretty much the proof of Stolkes Theorem given in Spivak
but I'm having a lot of difficulty understanding the details
specifically...when the piecewise function is defined for j>1 the integral is 0
and for j=1 the integral is nontrivial...why is it defined like that?
Also, I am having difficulty understanding what the inclusion map does (spivak defines it
as I(j,alpha) which is a continuous function or a chain of some sort) but the pull back
I*(j,alpha)fdx^1...dx^n is taken and integrated over in that piecewise function
could someone shed some light on that?
Thanks
that's pretty much the proof of Stolkes Theorem given in Spivak
but I'm having a lot of difficulty understanding the details
specifically...when the piecewise function is defined for j>1 the integral is 0
and for j=1 the integral is nontrivial...why is it defined like that?
Also, I am having difficulty understanding what the inclusion map does (spivak defines it
as I(j,alpha) which is a continuous function or a chain of some sort) but the pull back
I*(j,alpha)fdx^1...dx^n is taken and integrated over in that piecewise function
could someone shed some light on that?
Thanks