Vector Calculus Subscript Notation

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Discussion Overview

The discussion revolves around vector calculus subscript notation, particularly in the context of tensor calculus. Participants seek explanations and tutorials on how to interpret and apply this notation, including its relation to operations like divergence, gradient, and curl.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant requests a tutorial on vector calculus subscript notation, specifically mentioning examples like Eijk and Kklm.
  • Another participant suggests a resource, Heinbockel's text, which covers index notation in tensor calculus.
  • A participant expresses that while the suggested resource is helpful, it contains too much information and seeks a more general explanation of the fundamentals.
  • One participant shares their attempt to prove a specific identity involving the dot product of cross products and requests assistance with their calculations.
  • A different participant asks how to calculate Eijk (with ijk as subindices) multiplied by itself, stating that the expected value is 6 and seeking proof for this result.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the best resources for learning subscript notation or on the specific mathematical problems presented. Multiple competing views and approaches are evident in the discussion.

Contextual Notes

Some participants express uncertainty regarding the completeness of their mathematical proofs and the clarity of the notation used. There are unresolved steps in the calculations presented, and the discussion reflects varying levels of familiarity with the subject matter.

Who May Find This Useful

Readers interested in vector calculus, tensor calculus, and mathematical proofs involving vector operations may find this discussion relevant.

physics4life
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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 can't seem to find them. thnx
 
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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?
 
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
 
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
 

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