Vector Calculus Subscript Notation

1. Jul 26, 2007

physics4life

Hi there is there a tutorial or post explaining vector calculus subscript notation please?
e.g. Eijk Kklm

dil djm etc etc

is there a tutorial explaining these thoroughly and how these can convert into div grad and curl??
i've used the search engine but cant seem to find them. thnx

2. Jul 26, 2007

neutrino

3. Jul 26, 2007

physics4life

thanks a lot for that. it does help but there is far too much information there. i was just looking for a general explanation of the fundamentals and how the notations can be used to solve questions such as proving that:

grad(A.B) = (B.Delta)A + (A.Delta)B + BX(CurlA) + AX(CurlB)

etc etc... any suggestions please?

4. Aug 3, 2007

physics4life

im actually getting the hang of it now. but stuck on dot product of cross products..

e.g. show... (AXB) . (CXD) = (A.C)(B.D) - (A.D)(B.C)

here's what i have done but its partially correct.

$$(AXB)i = \varepsilon_{ijk}A_jB_k$$.
$$(CXD)i = \varepsilon_{ijk}C_jD_k$$

so (AXB) . (CXD) = $$(\varepsilon_{ijk}A_jB_k)_i . (\varepsilon_{ijk}C_jD_k)_i$$

= $$\varepsilon_{ijk}\varepsilon_{ijk}A_jC_jB_kD_k$$

= $$( \delta_{ij} \delta_{jk} - \delta_{ik}\delta_{jj})(A.C)_j(B.D)k$$

= $$[ \delta_{ij}(A.C)_j ][ \delta_{jk}(B.D)_k ] - [ \delta_{ik}(B.D)_k ][ \delta_{jj}(A.C)_j ]$$

= $$(A.C)_i(B.D)j - (B.D)_i(A.C)_j$$

=(A.C)(B.D) - (B.D)(A.C)

the first part of the answer (in red) i got right.. but the 2nd part is wrong as you can see

how am i meant to get -(A.D)(B.C)???