Gary
GaryVasco
Posts: 3,352 
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Post by Gary on Jan 25, 2017 16:42:24 GMT
Vasco,
True. He says "After you have read the next chapter, you will be able to look back at what we have just done and recognize it as an example of differentiating a complex function." I suppose that is what has just happened.
Gary
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Post by Admin on Jan 25, 2017 16:50:08 GMT
Vasco, True. He says "After you have read the next chapter, you will be able to look back at what we have just done and recognize it as an example of differentiating a complex function." I suppose that is what has just happened. Gary Gary When he says "just done" I take that as being a reference to the last two paragraphs of the subsection, from "Let us write $Z=(z-\xi_+)$..." on page 167, to the end of the subsection on page 168. Vasco |
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Gary
GaryVasco
Posts: 3,352
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Post by Gary on Jan 25, 2017 17:02:02 GMT
When he says "just done" I take that as being a reference to the last two paragraphs of the subsection, from "Let us write Z=(z−ξ+)..." on page 167, to the end of the subsection on page 168.
Vasco,
Probably so, but he is already applying that thinking in $\mathbb{P}$ 2, last sentence: "Thus the local effect of M ....", which is the part that provoked the comment from me.
Gary
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Post by Admin on Jan 25, 2017 18:18:46 GMT
When he says "just done" I take that as being a reference to the last two paragraphs of the subsection, from "Let us write Z=(z−ξ+)..." on page 167, to the end of the subsection on page 168. Vasco, Probably so, but he is already applying that thinking in $\mathbb{P}$ 2, last sentence: "Thus the local effect of M ....", which is the part that provoked the comment from me. Gary Gary I think he was probably trying to explain the local effect of $M$ without talking about differentiation, which would have been a distraction at that point and could have caused confusion, so he talked about the 'local effect' instead and then in chapter 4 he shows that the complex derivative IS the 'local effect' or amplitwist. Vasco |
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Gary
GaryVasco
Posts: 3,352
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Post by Gary on Jan 25, 2017 18:23:59 GMT
When he says "just done" I take that as being a reference to the last two paragraphs of the subsection, from "Let us write Z=(z−ξ+)..." on page 167, to the end of the subsection on page 168. Vasco, Probably so, but he is already applying that thinking in $\mathbb{P}$ 2, last sentence: "Thus the local effect of M ....", which is the part that provoked the comment from me. Gary Gary I think he was probably trying to explain the local effect of $M$ without talking about differentiation, which would have been a distraction at that point and could have caused confusion, so he talked about the 'local effect' instead and then in chapter 4 he shows that the complex derivative IS the 'local effect' or amplitwist. Vasco Vasco, That makes sense. Gary |
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