Post by Admin on May 10, 2016 20:37:44 GMT
Gary
As part of my commentary on section XI, I completed the suggested exercise near the bottom of page 254 asking for a proof of
$$f^{\dagger}(z)\equiv \overline{f\bigg(\frac{1}{\bar{z}}\bigg)}.$$
In the third and fourth lines from the bottom of page 254 Needham writes:
"By construction, this function sends symmetric pairs of points to conjugate images: $F^{\dagger}(z)=F(z)$". 'This function' refers to $F(z)$.
I immediately thought that it was strange to suddenly write $F^{\dagger}$ after writing $f^{\dagger}$ previously, and so I just wrote down the algebraic notation for the above quoted statement which in my opinion is:
$\overline{F(z)}=F(1/\bar{z})$
I then tried to prove it algebraically using the result of the last suggested exercise, shown at the top of this post, and I feel that I succeeded.
So in conclusion I would say that I feel reasonably sure that this is an error in the book, but I would like a second opinion before publishing it in the errata section. I thought you might have tried the suggested exercises etc on page 254, as your last post was about a later exercise. Any thoughts?
Vasco
As part of my commentary on section XI, I completed the suggested exercise near the bottom of page 254 asking for a proof of
$$f^{\dagger}(z)\equiv \overline{f\bigg(\frac{1}{\bar{z}}\bigg)}.$$
In the third and fourth lines from the bottom of page 254 Needham writes:
"By construction, this function sends symmetric pairs of points to conjugate images: $F^{\dagger}(z)=F(z)$". 'This function' refers to $F(z)$.
I immediately thought that it was strange to suddenly write $F^{\dagger}$ after writing $f^{\dagger}$ previously, and so I just wrote down the algebraic notation for the above quoted statement which in my opinion is:
$\overline{F(z)}=F(1/\bar{z})$
I then tried to prove it algebraically using the result of the last suggested exercise, shown at the top of this post, and I feel that I succeeded.
So in conclusion I would say that I feel reasonably sure that this is an error in the book, but I would like a second opinion before publishing it in the errata section. I thought you might have tried the suggested exercises etc on page 254, as your last post was about a later exercise. Any thoughts?
Vasco
