Useful Properties: (0 i ‡ j dij = (1 i = j) ê ê = dij à = :a¡êi Eijk = 1: (ijk) is an even (cyclic) permutation -1: (ijk) is an odd (non - cyclic) permutation 0: if two or more subscripts are the same 1 - €ijk = z (i − j) (j – k)(k − i) ê¡ x êj = €ijkêk Eijk = Ejki = Ekij Switching indices with even (cyclic) keeps the sign the same ¤ijk = −€jik = −Ekji Switching indices with odd (non-cyclic) reversed the sign a × b = a₁bj Eijkêk (à × b)k = a¡b¡ €¡jk X Eijk Elmk = Sil Sim δικ Sji Sjm Sjk Skl 8km 8kk Using the Properties above, reduce dijSjk Ski
Useful Properties: (0 i ‡ j dij = (1 i = j) ê ê = dij à = :a¡êi Eijk = 1: (ijk) is an even (cyclic) permutation -1: (ijk) is an odd (non - cyclic) permutation 0: if two or more subscripts are the same 1 - €ijk = z (i − j) (j – k)(k − i) ê¡ x êj = €ijkêk Eijk = Ejki = Ekij Switching indices with even (cyclic) keeps the sign the same ¤ijk = −€jik = −Ekji Switching indices with odd (non-cyclic) reversed the sign a × b = a₁bj Eijkêk (à × b)k = a¡b¡ €¡jk X Eijk Elmk = Sil Sim δικ Sji Sjm Sjk Skl 8km 8kk Using the Properties above, reduce dijSjk Ski
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Useful Properties:
(0 i ‡ j
dij = (1 i = j)
ê ê = dij
à = :a¡êi
Eijk
=
1: (ijk) is an even (cyclic) permutation
-1: (ijk) is an odd (non - cyclic) permutation
0: if two or more subscripts are the same
1
-
€ijk = z (i − j) (j – k)(k − i)
ê¡ x êj = €ijkêk
Eijk = Ejki = Ekij Switching indices with even (cyclic) keeps the sign the same
¤ijk = −€jik = −Ekji Switching indices with odd (non-cyclic) reversed the sign
a × b = a₁bj Eijkêk
(à × b)k = a¡b¡ €¡jk
X
Eijk Elmk
=
Sil Sim δικ
Sji Sjm Sjk
Skl 8km 8kk
Transcribed Image Text:Using the Properties above, reduce
dijSjk Ski
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