Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Vector Calculus Subscript Notation

  1. Jul 26, 2007 #1
    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. jcsd
  3. Jul 26, 2007 #2
  4. Jul 26, 2007 #3
    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?
  5. Aug 3, 2007 #4
    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.

    [tex] (AXB)i = \varepsilon_{ijk}A_jB_k[/tex].
    [tex] (CXD)i = \varepsilon_{ijk}C_jD_k[/tex]

    so (AXB) . (CXD) = [tex] (\varepsilon_{ijk}A_jB_k)_i . (\varepsilon_{ijk}C_jD_k)_i [/tex]

    = [tex]\varepsilon_{ijk}\varepsilon_{ijk}A_jC_jB_kD_k[/tex]

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

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

    = [tex](A.C)_i(B.D)j - (B.D)_i(A.C)_j[/tex]

    =(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)???
    thanks guys :) please help out
  6. Oct 9, 2011 #5
    Is there anybody who knows how to calculate Eijk(ijk is sbuindex) times itself. The value is 6 but I need to prove that. Thanks
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook