The 2° Stokes theorem?

1

Disclaimer: I’m a total beginner in GA (and in general mathematics), so if I’m saying something too wrong please or oblivious, please forgive me.

I’m reading the GA book for Electrical Engineers of Peeter Joot, and he introduces the generalized Stokes theorem:

\int_V d^k\cdot(\partial \wedge F) = \int_{\partial V} d^{k-1}\cdot F

Following the given proof, by grade selection on the fundamental theorem of GA, it seems to me that also the dual formulation should be right, doing similar proving steps:

\int_V d^k\wedge(\partial \cdot F) = \int_{\partial V} d^{k-1}\wedge F

So, is this formula known/correct?
Does this formula as a name?

Thanks for any help.

2

I believe that the Fundamental Theorem of Geometric Calculus is the sum of those 2 equations. Dot and wedge products are replaced with the geometric product. See A Survey of Geometric Algebra & Geometric Calculus - Macdonald, on his website, Alan Macdonald: Geometric Algebra and Foundations of Physics . It’s Equation 3.4 on page 23.

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I don’t think so. In general the product of two multivectors is not expressible like the sum of the dot and wedge product, right? So the right hand side is not the sum of the other two

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I’m sorry, you are right. My last post is in error.