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--- advanced_tools:exterior_derivative [2023/03/18 19:56]
edi [Intuitive]
+++ advanced_tools:exterior_derivative [2023/03/19 21:27]
edi [Intuitive]
@@ Line 8: / Line 8: @@
 In 3-dimensional space, the curl operator is equal to the [[advanced_tools:hodge_dual|Hodge dual]] of the exterior derivative: ${\rm curl}(v) = \star(\nabla \wedge v)$.
-The exterior derivative of a $p$-form $\omega$ is commonly written as $d\omega$. The result of $d\omega$ is a $p+1$-form.
+The exterior derivative of a $p$-form $\omega$ is commonly written as $d\omega$. The result of $d\omega$ is a ($p+1$)-form.
 Taking the exterior derivative twice (of any object) results in zero: $d^2\omega=0$. This is an important result with many implications for electrodynamics, topology, etc.