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Conway, Functions of One Complex Variable I
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Munkres, Topology
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Royden, Real Analysis
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Top 100 novels of all time
Reading Ulysses
IMDB top 250 films
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Vito Prosciutto: Teaching community college math on the road to a PhD.
Tuesday, May 24, 2005
15:04(Basic) Complex Analysis: Do I have this right?
At what points is the function f given by f(z)=x^{3}+i(1y)^{3} analytic? Explain.Since the points where the function has a derivative are two intersecting lines, my assumption is that there is no point where the function is analytic. Am I correct on this or am I making some really basic error?
Update: Hmm, going back over the function, the derivative that Cain gives for (1y)^{3} is wrong. I tried it using the chain rule, by evaluating (1y)^{3} and doing the derivative of the resulting polynomial and I even went to Quick Math and let their solver do it. And I was right, Cain was wrong: The derivative is 3(1y)^{2}, and not positive three. That and a quick internet search on analytic complex function reveals a definition which doesn't seem to match his. I'm thinking that perhaps I want to work with a different complex analysis book over the summer.