This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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; &amp; 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 &amp; j; RHS has j &amp; 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 &amp; 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 ....
View
Full
Document
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.
 Fall '09
 RENWEIMEI

Click to edit the document details