Introduction to cartesian tensors

[progiangbk]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

Plz help me, i don't understand what is the requirement ^^. Thanks very much!

 

[tiny-tim]

welcome to pf!

hi progiangbk! welcome to pf!

(try using the X² and X₂ buttons just above the Reply box )

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

Plz help me, i don't understand what is the requirement ^^. Thanks very much!

do you mean x₁² + 2x₁*x₂² + 3x₂²*x₃ ?

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

have you missed something out?​

 

[progiangbk]

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

In the same occasion, if you know the meaning of some symbols and eq to calculate the exercise 17 and 18 (in red rectangular), pls help me. Thanks !

 

[tiny-tim]

hi progiangbk!

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

ohh, the "i" is a subscript …

why didn't you say so?

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

_,i means ∂/∂x<sub>i

,ij</sub> means ∂²/∂x_i∂x_j

(so eg A_,i means the vector whose ith component is ∂A/∂x_i)

 

[Mark44]

Mod note: moving this thread to Calculus & Beyond.

 

[progiangbk]

Hi tiny-tim,

Thanks for your help.

Because I have just started to learned 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 completely, i can understand more, because I have many more exercise like that, so pls help ^

∂2/∂xi∂xj mean d2/dx1dx2 right?

thanks

 

[progiangbk]

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

Sorry, i have not been accustomed to this site

 

[tiny-tim]

hi progiangbk!

(just got up :zzz:)

∂2/∂xi∂xj mean d2/dx1dx2 right?

well, it only means that if i = 1 and j = 2

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

(this may help … http://en.wikipedia.org/wiki/Einstein_notation )

 

[progiangbk]

Thanks very much, i have submitted my HW he!