Gary
GaryVasco
Posts: 3,352 
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Post by Gary on May 30, 2016 6:06:46 GMT
Vasco, Here is an attempt at Exercise 26. nh.ch5.ex26.pdf (109.03 KB) (Revised June 2 in response to comments from Vasco) Gary |
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Post by Admin on May 30, 2016 8:14:13 GMT
Gary
I am still thinking about this exercise. I am not sure what Needham is looking for here in the first part of it. The second half about large values of $|z|$ seems more straightforward. For the moment I will not look at your solution.
Vasco
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Post by Admin on Jun 1, 2016 23:00:33 GMT
Gary
I have now had a go at exercise 26 which I will publish after finishing this post.
I have looked at your solution and I think there are a couple of things that I have a problem with:
1) $\mathfrak{R}_E\circ\mathfrak{R}_E$ is the identity always, even when the interior and exterior are not swapped.
2) I think the reason this doesn't work for $z=2.5+1.6i$ is because you are not using the correct branch of the complex square root function in certain situations.
I had the same problem with my spreadsheet.
Do you remember exercise 24 in chapter 2, when I seem to remember you were using the arctan function, and because it is a multifunction, the standard function of Mathematica was giving you inappropriate values? I think this is a similar problem in many ways.
Have a think about it and then we can go into more detail.
Vasco
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Gary
GaryVasco
Posts: 3,352
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Post by Gary on Jun 1, 2016 23:51:23 GMT
Vasco,
Both your points now seem valid to me. I'll have another look.
Gary
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Gary
GaryVasco
Posts: 3,352
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Post by Gary on Jun 2, 2016 23:32:29 GMT
Vasco,
The original attempt has been replaced with a revision.
Gary
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Post by Admin on Jun 3, 2016 15:33:09 GMT
Gary
I will take a look as soon as I can and get back to you.
Vasco
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