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Eulers Formula






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phoenix3200

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e^(i*x)=cos(x)+i*sin(x)

e^(i*pi)=cos(pi)+i*sin(pi)=-1.

It gets used a lot when solving quantum mechanics problems. My college math teacher loved that equation - it's got every important mathematical value in it.
 
pullbangdead

pullbangdead

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Niko said:
[quote author=pullbangdead link=1226831007/0#8 date=1227082462]^Except for some people, like electrical engineers, the imaginary number -1^(1/2) is j.  I mean, I understand why they do that wiht electrical current being represented by i already, but still, WHY DO THEY DO THAT?!??  Ugh.

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You get into some crazy variable assignments when you get into advanced topics.  The more advanced you get, the more letters you need, and there just aren't enough.  With the classes I have now, we literally have used most of all of the following letters: lower case english, script lower case english, upper case english, script uppercase english, lowercase greek, and uppercase greek.  You know how hard it is to tell the difference between a lowercase greek "eta" and a lowercase script english letter "n" in my handwriting?  And keeping a single formula going in a derivation which includes multiple cases of each of uppercase greek sigma, uppercase english E, and uppercase script english E.  Not to mention variables can all have subscripts, superscripts, bars on top, tildas on top (this---> ~), or multiple of those.  Just reading notes makes my head hurt these days.

I've had a class previously where one of our main formulas we had to remember how to use and expand multiple ways was literally x[sup]x[/sup] = X.  All of them being the letter x: one lowercase, one lowercase script, and one uppercase, and all meaning VERY different things.
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Dude, -1^1/2 is the same as sqrt (-1)

the thing is that when working with electronics you call it 'j' because you call 'i' the current intensity and it could create confusion.



i've never seen that formula, not even in college....i went past thru taylor, maclaurin, series, etc... but never seen euler =([/quote]

I know, that's what I was saying. It is the same number, but electrical engineers insist on using a different letter than everyone else. To everyone else on earth, that number is "i". To electrical engineers, it's "j". They use "i" for current, yes, but they also use "j" for current density, or other things as well. You still have to use context to see what each one stands for no matter what, so why can't they just do what everyone else does and use "i" for imaginary numbers? Since we're still having to use context to decide what something means, then they might as well have the context be the same as every other discipline on campus.
 
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nikokapo

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i guess it's just the way it is taught on every classroom around the world..

i'm sure there must be one or two professors that do not want
images
like using 'j'.
 
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