(Daniel Castillo's Favorite Theorem) |
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Let D be a simple region and let C be its boundary. Suppose P: D -> '''R''' and Q: D -> '''R''' are of class C1. Then | Let D be a simple region and let C be its boundary. Suppose P: D -> '''R''' and Q: D -> '''R''' are of class C1. Then | ||
| − | <math>\int_C+^ \P * dx + Q * dy = \int_\int_D ((part(Q) / part(x) - part(P) / part(y))) * dx * dy.</math> | + | <math>\int_C+^ \P * dx + Q * dy = \int_\int_D \((part(Q) / part(x) - part(P) / part(y))) * dx * dy.</math> |
Revision as of 13:44, 21 January 2009
Daniel Castillo's Favorite Theorem
My favorite theorem is Green's Theorem. Here it is as it is stated in Jerrold E. Marsden & Anthony J. Tromba's Vector Calculus:
Let D be a simple region and let C be its boundary. Suppose P: D -> R and Q: D -> R are of class C1. Then
$ \int_C+^ \P * dx + Q * dy = \int_\int_D \((part(Q) / part(x) - part(P) / part(y))) * dx * dy. $
