Help with Beginner Index Notation

AI Thread Summary
The discussion focuses on understanding index notation in the context of vector calculus, specifically the curl of a product of a scalar field and a vector field. The user is tasked with proving that curl(fF) equals fcurl(F) plus the cross product of the gradient of f and F. A suggested approach involves applying the chain rule and using the Levi-Civita symbol for the curl operation. Participants emphasize the importance of correctly using notation, such as subscripts for indices. The conversation aims to clarify the mathematical steps needed to solve the problem effectively.
fttteotd
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Okay, so I'm learning some basic index notation, and I have a few questions...

Homework Statement


f= scalar field
F = vector field

so, we are supposed to show that curl(fF) = fcurl(F) + (\nablaf) x F

The Attempt at a Solution



curl(fF) = [\nabla x (fF))]_{k} = \in_{ijk}(f\partial_{i}F_{j} + F_{j}\partial_{i}f)

any help??

(all the superscripts are supposed to be subscripts, i dunno)
 
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Welcome to PF!

Hi fttteotd! Welcome to PF! :smile:

(have a curly d: ∂ and a nabla: ∇ and an epsilon: ε and use itex rather than tex in the middle of a line :wink:)

[∇ x (fF)]i = εijk∂j(fFk) …

and now use the chain rule! :wink:
 

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