Wedge Product of Differentials in Integration
Can someone explain the difference between and ?
In general, is ?
Does Fubini's Theorem disregard orientation, instead working solely with a measure space without assuming additional structure?
I've been trying to figure this out, and now I have a headache from trying to read stuff about it because it uses some weird physics prefix notation. (Worried)
Any help is greatly appreciated. Thank you.
Re: Wedge Product of Differentials in Integration
There is no difference except, as you suggest, orientation. is the integral on a surface with the normal oriented in the direction of . is the integral on a surface with the normal oriented in the direction of . In "Calculus III" integration, the orientation is assumed to be given as part of the limits of integration.