Complete set of answers to Schaum's Tensor Calculus

In summary, two individuals, JTMetz and TerryW, have corresponded about working through Schaum's Tensor Calculus by Kay. JTMetz is attempting to work through every solved and supplementary problem in his spare time while TerryW has already completed all the problems and supplementaries. JTMetz has asked about an errata webpage or document and if anyone has worked out the answers to the supplementary problems. TerryW responds that there are likely errors in the book and he has attempted to contact the publishers with no response. He offers to correspond electronically and suggests using PF for communication due to its use of LaTex. Another individual, Phil B, joins the conversation and asks for help with a specific problem. TerryW provides a hint and
  • #1
JTMetz
1
1
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.
 
  • Like
Likes chad mcelroy
Physics news on Phys.org
  • #2
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
 
  • Like
Likes atyy
  • #3
I'm afraid he was last here a decade ago.
 
  • Haha
Likes suremarc
  • #4
Thanks for letting me know.

Maybe my post will result in an email and perhaps inspire him to reopen his Schaum!RegardsTerryW
 
  • #5
TerryW said:
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
 
  • #6
Phil B said:
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
 
  • Like
Likes Phil B
  • #7
Thanks for that. I look forward to your help.

Regards,

Phil
 
  • #8
TerryW said:
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
 
  • #9
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.
 
  • #10
Phil B said:
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
 
  • #11
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
 

Attachments

  • Maths photo.jpg
    Maths photo.jpg
    37.1 KB · Views: 170
  • #12
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
 
  • #13
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
 
  • Like
Likes berkeman
  • #14
Hi Phil,
Glad to hear that it is all sorted now.

RegardsTerryW
 
  • Like
Likes berkeman

1. What is Schaum's Tensor Calculus?

Schaum's Tensor Calculus is a comprehensive guidebook that covers all the essential topics and concepts in tensor calculus. It is designed to help students understand the principles and applications of tensor calculus in a clear and concise manner.

2. Is this book suitable for beginners?

Yes, this book is suitable for beginners who have a basic understanding of calculus and linear algebra. It is written in a way that is easy to follow and includes many examples and exercises to help readers grasp the material.

3. How is this book different from other textbooks on tensor calculus?

Schaum's Tensor Calculus provides a complete set of answers to all the problems in the main textbook, making it a valuable resource for self-study and exam preparation. It also includes additional examples and explanations to enhance understanding.

4. Can this book be used as a supplement to a course on tensor calculus?

Yes, this book can be used as a supplement to a course on tensor calculus. It covers all the essential topics and provides detailed explanations and examples, making it a useful resource for students looking to reinforce their understanding of the subject.

5. Are there any prerequisites for using this book?

Some basic knowledge of calculus and linear algebra is recommended before using this book. It is also helpful to have a basic understanding of vector calculus and differential equations, although these topics are covered in the book as well.

Similar threads

I A couple questions about the Riemann Tensor, definition and convention
    • Differential Geometry
Replies
2
Views
2K
Studying Ready to start Calculus (I think), but unsure where to start
    • STEM Academic Advising
Replies
29
Views
2K
Geometry "The Geometry of Physics" - Theodore Frankel
    • Science and Math Textbooks
Replies
6
Views
2K
I Wish to Give Away a Textbook Set on The Calculus
    • Science and Math Textbooks
Replies
9
Views
1K
James Stewart Calculus replacement
    • Science and Math Textbooks
Replies
12
Views
2K
Struggling immensely with tensors in multivariable calculus
    • Calculus and Beyond Homework Help
Replies
5
Views
2K
I Completeness relations in a tensor product Hilbert space
    • Quantum Physics
Replies
13
Views
2K
I Motivating definitions in calculus on manifolds
    • Calculus
Replies
2
Views
1K
Einstein's applications of tensor calculus
    • Calculus
Replies
5
Views
3K
Understanding Tensors for General Relativity: A Comprehensive Guide
    • Special and General Relativity
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top