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Introduction to cartesian tensors

  1. Mar 26, 2012 #1
    1. The problem statement, all variables and given/known data

    This exercice is in a Chapter named Introduction to Cartesian tensors. The following is the original question of the exercise:

    2. Relevant equations

    Compute the vector: (x1^2 + 2x1*x2^2 + 3x2^2*x3), i

    3. The attempt at a solution

    Plz help me, i dont understand what is the requirement ^^. Thanks very much!!!
     
  2. jcsd
  3. Mar 26, 2012 #2

    tiny-tim

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    welcome to pf!

    hi progiangbk! welcome to pf! :smile:

    (try using the X2 and X2 buttons just above the Reply box :wink:)
    do you mean x12 + 2x1*x22 + 3x22*x3 ?

    but that's not a vector, it's a scalar :confused:

    have you missed something out?​
     
  4. Mar 26, 2012 #3
    No, please see the expression again, there is a bracket pair and i symbol at the end: (x1^2 + 2x1*x2^2 + 3x2^2*x3), i

    I have uploaded the picture of the exercise 16: http://img252.imageshack.us/img252/4437/66167045.png [Broken]

    In the same occassion, if you know the meaning of some symbols and eq to calculate the exercise 17 and 18 (in red rectangular), pls help me. Thanks !!!!
     
    Last edited by a moderator: May 5, 2017
  5. Mar 26, 2012 #4

    tiny-tim

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    hi progiangbk! :smile:

    (please use the X2 and X2 buttons just above the Reply box :wink:)

    ohh, the "i" is a subscript

    why didn't you say so? :redface:

    you mean (x12 + 2x1*x22 + 3x22*x3)i ?

    ,i means ∂/∂xi

    ,ij means ∂2/∂xi∂xj

    (so eg A,i means the vector whose ith component is ∂A/∂xi)
     
  6. Mar 26, 2012 #5

    Mark44

    Staff: Mentor

    Mod note: moving this thread to Calculus & Beyond.
     
  7. Mar 26, 2012 #6
    Hi tiny-tim,

    Thanks for your help.

    Because I have just started to learnt this subject and the author of the book has written like that so I copy original version only :P please see the picture! i have understood something after reading your answer but if you can do it completly, i can understand more, because I have many more exercise like that, so pls help ^

    ∂2/∂xi∂xj mean d2/dx1dx2 right?

    thanks
     
  8. Mar 26, 2012 #7
    (please use the X2 and X2 buttons just above the Reply box )

    Sorry, i have not been accustomed to this site
     
  9. Mar 27, 2012 #8

    tiny-tim

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    hi progiangbk! :smile:

    (just got up :zzz:)
    well, it only means that if i = 1 and j = 2

    2/∂xi∂xj is a general formula, for any values of i and j (= 1 2 or 3, possibly the same) :wink:

    (this may help … http://en.wikipedia.org/wiki/Einstein_notation )
     
  10. Apr 1, 2012 #9
    Thanks very much, i have submitted my HW he!
     
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