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Curl of the product of a scalar and a vector using Levi-Civita

Friday, July 1st, 2011

By Eliezer Estrecho To prove this formula, we use the following: Where: and Using the equation above: We can factor out in the first term to give: Note that for the second term, the permutation of indices are odd, rearranging them to ijk will give the negative: Thus, About the author: Eliezer Estrecho is currently […]

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Proving Vector Identity Involving the Unit Vector Using the Levi-Civita and the Kronecker Delta

Wednesday, June 29th, 2011

*author: Michelle R. Fudot   Prove: ___________________________________________________________ Proof: First, we define the following vectors as: ; ; and Now,  if we let i=k, then . Furthermore, Now, the derivative of orthonormal basis , that is, and the derivative of a coordinate X, . Also, , thus = = = = It is noted that . […]

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Vector Analysis

Wednesday, June 29th, 2011

Prove: where:     Sol’n:   then:             or      

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Curl of the Gradient of a Scalar

Wednesday, June 29th, 2011

proof that the curl of the gradient of a scalar function is equal to zero let and

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Proving Vector Identity Using Levi-Civita Symbol

Tuesday, June 28th, 2011

Roel N. Baybayon MSPhysics1 ————————————————————————————————– We are going to prove the following vector identity using Levi-Civita symbol: Solution: Let    ,     ,   ,   . Then, By definition: We have to let m=n so that, Levi-Civita symbol can be expressed in terms of Kronecker delta given by: Thus,    

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