Solution%20to%20HW#1

Solution%20to%20HW#1 - EGM 6812/ Fluid Mechanics I Homework...

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Unformatted text preview: EGM 6812/ Fluid Mechanics I Homework # 1 Due Sept. 4, 2009 1. Given: Following expressions were a, b, c, d, and e are arbitrary quantities. a = b i c ij d j a = b i +c ij d ji e i a = b i c i d+d j a l = ijk b j c k a i = ij b i +c i a ij = b ji a k = b i c ki a ij = b i c j +e jk a k = b k c i + d i e ik a k l = b i c ki d l +e k l Find: Expressions that are allowed in index notation Solution: a = b i c ij d j : Yes (i and j are dummy) a = b i +c ij d ji e i : No (LHS has no free index, RHS has i; & i appears 3 times) a = b i c i d+d j : No (LHS has no free index; RHS free index from d j ) a l = ijk b j c k : No (LHS has free index l , RHS has i; not matching) a i = ij b i +c i : No (LHS has free index i. ij b i on RHS has a free index j) a ij = b ji : Yes a k = b i c ki : Yes a ij = b i c j +e jk : No (LHS has free indices i & j; RHS has j & k from e jk ) a k = b k c i +d i e ik : No (LHS has free index k; b k c i has free indices k & i) a k l = b i c ki d l +e k l : Yes. 2. Use the notation of indices to derive the following: a) x =3 and (A B ) = [ i i j B A x + i i j A B x ] e j ....
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This note was uploaded on 09/09/2010 for the course EGM 6812 taught by Professor Renweimei during the Fall '09 term at University of Florida.

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Solution%20to%20HW#1 - EGM 6812/ Fluid Mechanics I Homework...

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