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Post by Admin on Apr 12, 2016 11:54:29 GMT
I have finally managed to finish exercise 17 parts (i) - (vi). It contains four appendices as well as my solutions to parts (i) - (vi).
It is quite a large document - about 36 pages - and I am sure that there must be one or two errors/typos in there somewhere, so if you find any, or think you have found some, please post the details on this forum and I will make any necessary corrections.
Vasco
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Post by telemeter on Mar 1, 2019 16:28:36 GMT
Hi there. Just out of interest it seems to me that you can go much more directly to the results for part i) by using the equation for curvature at the top of page 238 ( beginning of section 3). As the derivatives for exp(x) are all the same and k=0, then for k tilde to vanish you just need Im (xi) to vanish.ie xi has to be real only.
Personally, I didn't have a problem with the wording of part ii).
The answers to part iv) rapidly drop out (in a couple of lines) by using the same approach as i) using that same p238 equation.
v) drops out a bit easier if as a first step one shifts the origin to -d/c then the differentials are easier as M(z) simplifies to a function of 1/z...and again using the p238 equation.
Apologies if I am just saying the obvious.
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Post by Admin on Mar 1, 2019 17:04:51 GMT
Hi
Welcome to the forum!
Note that the first part of this exercise asks us not to use calculation. Then part (iii) asks us to verify our result in (i) by using (28). So we should avoid using the formula on page 238 until then. The whole point of doing this exercise 'without calculation' is to gain geometric insights and not just substitute into a formula!
Are you going to publish your solution so that we can give you some feedback?
Vasco
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Post by telemeter on Mar 2, 2019 18:38:13 GMT
I take your point. Very often I find my very literal approach can lead me astray. This did not need actual calculation...it was just immediately intuitively obvious, exp(x) being a familiar friend.
Excellent work on all the solutions. Really appreciate the effort involved.
I do my answers on a whiteboard as I go through the book so don't have a record of them for posting.
I note you have a couple of gaps...let me know if any thoughts would be appreciated but I understand totally if not.
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Post by Admin on Mar 3, 2019 17:16:48 GMT
I take your point. Very often I find my very literal approach can lead me astray. This did not need actual calculation...it was just immediately intuitively obvious, exp(x) being a familiar friend. Excellent work on all the solutions. Really appreciate the effort involved. I do my answers on a whiteboard as I go through the book so don't have a record of them for posting. I note you have a couple of gaps...let me know if any thoughts would be appreciated but I understand totally if not. Hi Thanks. Yes still working on some of the exercises. I prefer to work on them myself, but I welcome comments on my published solutions. There are a few exercises which seem to be incorrectly stated in the book eg Ex. 25 of chapter 6. I'm not sure how far you have reached in the book, but if you have an opinion on whether this exercise makes sense or not it would be nice to know. Vasco |
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