Vector Analysis Review for Mechanics course

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warwick

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Jan 27, 2006
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I got an A in my Vector Analysis course last semester. I'm not sure why I'm having trouble now reviewing Vector Analysis in my Intermediate Mechanics course. :cry:

20. Someone worked it out in class today, but they started with a different set of indices. The question has ijk and ljk, not ijk and lmk. In the middle of the problem they changed m to j so that it mirrors ijk and ljk. Is that valid?

http://i111.photobucket.com/albums/n149 ... 1283207581

http://i111.photobucket.com/albums/n149 ... 1283209810

26. I'm not even sure which coordinate system to use. Do I use spherical and set d-phi to zero (plane polar)? I'm very lost on this one.

http://i111.photobucket.com/albums/n149 ... 1282967742

28.

http://i111.photobucket.com/albums/n149 ... 1282967285

http://i111.photobucket.com/albums/n149 ... 1283212515

31. I didn't get (a), and I got a negative for (c). I don't know how to do (b).

http://i111.photobucket.com/albums/n149 ... 1282967605

http://i111.photobucket.com/albums/n149 ... 1283212418

http://i111.photobucket.com/albums/n149 ... 1283212277
 
warwick said:
I got an A in my Vector Analysis course last semester. I'm not sure why I'm having trouble now reviewing Vector Analysis in my Intermediate Mechanics course. :cry:

20. Someone worked it out in class today, but they started with a different set of indices. The question has ijk and ljk, not ijk and lmk. In the middle of the problem they changed m to j so that it mirrors ijk and ljk. Is that valid?

http://i111.photobucket.com/albums/n149 ... 1283207581

In the above problem you are "summing over" j & k - those are called dummy indices. Those can be changed to any name wish (other than i & l - the remaining indices). BTW, you are doing Tensor analysis now - not Vector

http://i111.photobucket.com/albums/n149 ... 1283209810

26. I'm not even sure which coordinate system to use. Do I use spherical and set d-phi to zero (plane polar)? I'm very lost on this one.

http://i111.photobucket.com/albums/n149 ... 1282967742

31. I didn't get (a), and I got a negative for (c). I don't know how to do (b).

http://i111.photobucket.com/albums/n149 ... 1282967605

I'm working on uploading my work.

28.

http://i111.photobucket.com/albums/n149 ... 1282967285

I'm working on uploading my work.
Click to expand...
 
Subhotosh Khan said:
In the above problem you are "summing over" j & k - those are called dummy indices. Those can be changed to any name wish (other than i & l - the remaining indices). BTW, you are doing Tensor analysis now - not Vector
Click to expand...

So, my analysis of what they did was correct? And I can always play with the dummy indices to get into a more familiar and workable form?

Also, I posted the rest of my work in the first post.

Here's my work for 31.a. I'm not close.

http://i111.photobucket.com/albums/n149/camarolt4z28/31a.jpg?t=1283118115

Here's my work for 38. I had to bust out my calculus textbook to look up the procedure for Stokes's Theorem for surface integral evaluation.

38. Find the value of the integral - surface integral curl A dot da, where A = yi + zj + xk and S is the surface defined by the paraboloid z = 1 - x^2 - y^2.

http://i111.photobucket.com/albums/n149/camarolt4z28/38a.jpg?t=1283118127

http://i111.photobucket.com/albums/n149/camarolt4z28/38b.jpg?t=1283118138
 
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