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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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Verifying vector formulas using Levi-Civita: (Divergence & Curl of normal unit vector n)

Tuesday, June 28th, 2011

By Sim P. Bantayan, MS Physics I, MSU-IIT Let , and where and .   1. Prove that . Proof: Now, . Since i=j for the divergence of normal unit vector n, but (i=j). Moreover, for three dimensions, , so Therefore, .   2. Prove that . Proof: . Since i=j for the curl of normal unit vector n, […]

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Proving Vector Formula with Kronecker Delta Function and Levi-Civita Symbol

Tuesday, June 28th, 2011

Applying and in Proving the Vector Formula:  By: Quennie J. Paylaga   Prove: using Kronecker Delta Function and Levi-Civita Symbol.     To prove this, we let We can write the expression for in summation form as:      where where i, j, l are dummy summation variables. Each of which can be any letter […]

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