Complete set of answers to Schaum's Tensor Calculus

[JTMetz]

I am studying Schaum's Tensor Calculus by Kay. I am attempting to work through every solved problem (covering up the answers, first) and every supplementary problem. I am not a student. My day job is computational chemistry, so I can only do this in my spare time (whatever that is!).

A few questions: 1) Is there an errata webpage or document anywhere? 2) Is anyone aware of webpages or documents that have worked out answers (with some helpful commentary), especially for the supplementary problems? 3) Is there anyone out there, like me who already has, or who is in the process of working through the problems, and would like to correspond electronically, rather than pester folks via this forum?

Please note that I have attempted to contact Kay directly (he is now retired), but have received no response.

 

[TerryW]

Hi JTMetz,

I've just come across your post more or less by accident. I have worked my way through Schaum and (I think) have done all the problems and supplementaries. I reckoned that there were loads of errors in the book, mainly bad typesetting and poor proof reading and I sent an email off to the publishers but never received a reply. I'm happy to be pestered if you are still around and interested. PF is best for communication because of the use of LaTex for all the subscripting, symbols etc.

RegardsTerryW

 

[Vanadium 50]

I'm afraid he was last here a decade ago.

 

[TerryW]

Thanks for letting me know.

Maybe my post will result in an email and perhaps inspire him to reopen his Schaum!RegardsTerryW

 

[Phil B]

Hi JTMetz,

I've just come across your post more or less by accident. I have worked my way through Schaum and (I think) have done all the problems and supplementaries. I reckoned that there were loads of errors in the book, mainly bad typesetting and poor proof reading and I sent an email off to the publishers but never received a reply. I'm happy to be pestered if you are still around and interested. PF is best for communication because of the use of LaTex for all the subscripting, symbols etc.

RegardsTerryW

Hello TerryW,
I'm working through the questions in Schaum, but am struggling with 6.29. Using the method of Q 6.6 gets me stuck. I would be grateful for any tips on this.

Regards.

Phil B

 

[TerryW]

Hello TerryW,
I'm working through the questions in Schaum, but am struggling with 6.29. Using the method of Q 6.6 gets me stuck. I would be grateful for any tips on this.

Regards.

Phil B

I'll have to dig out my old notes and get back to you on this.

RegardsTerryW

 

[Phil B]

Thanks for that. I look forward to your help.

Regards,

Phil

 

[TerryW]

I'll have to dig out my old notes and get back to you on this.

RegardsTerryW

Hi Phil B

Have you noticed that in Question 6.6, $x^i$ is rectangular and $\bar x^i$ is curved but in 6.29 this is reversed?

This means that in "An Important Formula" (6.6) the barred Christoffel symbol belongs to the rectangular system and is therefore zero.

This gives you two partial derivative equations. If you can solve these analytically, you are better at maths than me! All I did at this point was to "guess" the co-ordinate functions $\bar x^i (x^i, x^j)$ and then work out all the partial derivatives needed to check that the two equations are consistent.

I chose to generalise the co-ordinate functions later once I had worked through the simple case of coincident origins/axes.

Hope this hint helps. There is one further pitfall you might or might not encounter.RegardsTerry W

 

[Phil B]

I interchanged the barred and unbarred symbols in (6.6), so that the newly barred Christoffer symbol, which now applies to the rectangular system, is therefore zero, and the second term on the right disappears. This gave me three PDEs to solve, one of which had zero on the right hand side.

 

[TerryW]

I interchanged the barred and unbarred symbols in (6.6), so that the newly barred Christoffer symbol, which now applies to the rectangular system, is therefore zero, and the second term on the right disappears. This gave me three PDEs to solve, one of which had zero on the right hand side.

Hi Phil,

I didn't swap the barring in (6.6) and it worked out fine, but it also works out OK if you do change the barring (and it is a bit easier!)

If you don't want to bother with Latex, could you send me a photo of a page with your three PDEs.

RegardsTerry

 

[Phil B]

Hi Terry,

I don't have Latex, so attach a photo of my working leading to three PDEs.

Hope you can decipher my writing!

Regards,

Phil

 

[TerryW]

Hi Phil,

Your three equations are fine, but you need to take them another step forward. Put r = 1 or r = 2 into each equation making six equations in all.

When I used the original version of (6.6), the resulting equations didn't look like I'd be able to produce the required results for the relationships $\bar x^i = \bar x^i(x^i, x^j)$ so I "guessed" the answer and checked out that all my equations balanced.

The three (x2) equations you have produced using the version of (6.6) with the barring interchanged, leads to a set of equations which I now believe can be used analytically to produced the required results.

Note that the two equations derived from putting r = 1 and r = 2 into your equation 3 actually provide you with quite a bit of information about $\bar x^i = \bar x^i(x^i, x^j)$!RegardsTerry

 

[Phil B]

Thanks Terry. After a break from maths, I had another go at this and found that the answer in the book certainly agrees with my 6 equations. Not sure I would have got there on my own though!

Regards,

Phil

 

[TerryW]

Hi Phil,
Glad to hear that it is all sorted now.

RegardsTerryW