Gary
GaryVasco
Posts: 3,352 
|
Post by Gary on May 12, 2016 2:20:25 GMT
Vasco, In your archived document on p. 1, last sentence, you have “(1) expresses the relationship between $\tilde{z}$ and $\overset{-}{z}$, symmetric points in L (reflections of each other in L.)” The equation does express the relationship, but I don’t think $\tilde{z}$ and $\overset{-}{z}$ are symmetric in L. I did the problem, taking my lead from your answers in places, but there are a few differences. nh.ch5.ex27.pdf (167.14 KB) Gary |
|
|
|
Post by Admin on May 12, 2016 18:48:52 GMT
Vasco, In your archived document on p. 1, last sentence, you have “(1) expresses the relationship between $\tilde{z}$ and $\overset{-}{z}$, symmetric points in L (reflections of each other in L.)” The equation does express the relationship, but I don’t think $\tilde{z}$ and $\overset{-}{z}$ are symmetric in L. I did the problem, taking my lead from your answers in places, but there are a few differences. View AttachmentGary Gary Thanks for pointing out my error. I will remove the offending phrase. I like your answers, especially for part (iii) using the fact that applying the mapping twice should be the identity mapping. Vasco |
|
Gary
GaryVasco
Posts: 3,352
|
Post by Gary on May 14, 2016 14:46:53 GMT
Vasco,
Thank you. I’m still rereading and pondering the section on analytic continuation via reflections.
Gary
|
|
|
|
Post by Admin on May 14, 2016 15:44:23 GMT
Gary
I'm trying to finish off my commentary on that very section, shouldn't be too long. I am finding it necessary to fill in a lot of the detail that Needham has left out - very like the section on curvature.
After this chapter what do you fancy doing next? As you will no doubt have noticed I have done quite a few of the exercises for the chapters on integration - 8 and 9. I did them without reading chapter 7, which I would like to do at some point as it is relevant to chs. 8 and 9. Chapter 6 is very interesting and quite long. It is marked by Needham as a chapter that can be skipped on first reading. I am quite happy to do any of them, even going straight to 8 and 9 if that's what you fancy doing next. I could attempt to do the exercises I left undone first time around.
Vasco
|
|
Gary
GaryVasco
Posts: 3,352
|
Post by Gary on May 14, 2016 22:34:48 GMT
Vasco,
I am quite happy to proceed straight through without skipping anything. I don't think I have ever done that when taking a math course and I am enjoying the feeling of coming to new problems knowing that I have acquired the prerequisites. Needham is very good at writing problems that require concepts from previous chapters. Besides, I think the goal for both of us is to understand Penrose's theories of cosmology and quantum physics, and chapter 6 appears to be essential in that regard. But first I have to finish several problems in chapter 5.
Gary
|
|
