yeah, I took complex analysis and it's surprising who gets freaked out by that---I don't think most engineers, even EEs, see complex analysis as undergrads at all anymore, which is just wrong---but it won't help you recognize 3sin(z) - 4sin^3(z) as sin(3z). Doing that with complex exponentials is a lot more algebra.
integrating x^x, that's cute. I know I've seen it before, ages ago, but man is that pathological. Silly interview question though.
I freely admit I had to googlephygelusApril 12 2006, 07:02:30 UTC
it's a classic trick question, like integrating sin(x)/x, you have to do it numerically or at least with a series expansion, and you have to pay attention to where it misbehaves. Cute what it does between negative integers, huh?
The wrong way to do it, which is what I would have done in an interview, unprepared, is to rewrite it as e^(x*log(x)) and then try to integrate by parts or something.
There's a cute problem in the beginning of "Numerical Methods That Usually Work" that is pretty much the simplest geometric/trigonometric problem you have to solve numerically. Of course I went roundy-round on it thinking "well I could write the series expansion but there's got to be a closed-form solution" hahahahah
So I guess the moral of the story is, know your series expansions for at least the transcendental functions cold too. Or at least be real ready to go there.
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integrating x^x, that's cute. I know I've seen it before, ages ago, but man is that pathological. Silly interview question though.
Reply
(The comment has been removed)
The wrong way to do it, which is what I would have done in an interview, unprepared, is to rewrite it as e^(x*log(x)) and then try to integrate by parts or something.
There's a cute problem in the beginning of "Numerical Methods That Usually Work" that is pretty much the simplest geometric/trigonometric problem you have to solve numerically. Of course I went roundy-round on it thinking "well I could write the series expansion but there's got to be a closed-form solution" hahahahah
So I guess the moral of the story is, know your series expansions for at least the transcendental functions cold too. Or at least be real ready to go there.
Reply
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