Chapter1 - AE 321 Practice Problems Chapter 1: Mathematical...

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AE 321 – Practice Problems Chapter 1: Mathematical Preliminaries 1. How many terms (and why) are represented by: A ij B ij , kl C ij , ji D ijk A pq B qr 2. How many equations (and why) are represented by: A ij B jk C kl = D il A ij , j = 0 A ijk , l + B ij , kl = C ijkl 3. Write out the following using standard (longhand) notation A ij B jk = C ik A i = B i , k C k 4. Compute the following expressions (where δ is the Kronecker delta): ! ij ij = ? ij jk ki = ? 5. Given the identity, ijk pqr = det " ip iq ir jp jq jr kp kq kr # $ % % % % ( ( ( ( where ε is the alternator and is the Kronecker delta, use indicial notation to find the simplest expressions for: (i) ijk iqr = (ii) ijk ijr = (iii) ijk ijk = . 6. If a , b and c are vectors, use indicial notation to prove the following vector identities: a ! b ( ) c = a b ! c ( ) a ! b ( ) ! c = a c ( ) b- b c ( ) a a ! b ( ) a ! b ( ) = a a ( ) b b ( ) " a b ( ) 2
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This note was uploaded on 09/18/2008 for the course AE 321 taught by Professor Waller during the Fall '07 term at University of Illinois at Urbana–Champaign.

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Chapter1 - AE 321 Practice Problems Chapter 1: Mathematical...

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