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Hi, I am interested in taking a complex analysis course. How useful is it to the physical sciences?

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- Thread starter jaejoon89
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In summary, Complex analysis is a course that deals with complex numbers and their applications in mathematics and physics. While it may not be necessary for all areas of physics, it can be useful in understanding concepts such as the Cauchy-Riemann conditions and the calculus of residues. However, some students find that they can learn these concepts through other courses or self-study, and may instead choose to focus their time on other topics such as group theory. Ultimately, the usefulness of a complex analysis course depends on the individual's academic and career goals.

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Hi, I am interested in taking a complex analysis course. How useful is it to the physical sciences?

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Cauchy-Riemann conditions are somewhere else you'll run into complex numbers. I'm sure there are a million more examples.

Now while i do use complex analysis quite often i never took a coarse in it and i am surviving quite fine. However, i would say that if it looks interesting go for it! It will definitely be useful at some point.

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Lambduh said:

Cauchy-Riemann conditions are somewhere else you'll run into complex numbers. I'm sure there are a million more examples.

Now while i do use complex analysis quite often i never took a coarse in it and i am surviving quite fine. However, i would say that if it looks interesting go for it! It will definitely be useful at some point.

you're probably just using the complex expression of the Fourier series which isn't really complex analysis.

anyway having just finished my complex "variables" final, an applied complex analysis class, i can tell you that the only useful thing i got out of it was the calculus of residues and laurent series. so yea. skip that class and just learn how to use/do those two things. of course for both those things you'll need to understand things like analytic functions and the cauch riemann equations. we spent half a semester covering stupid things like how to take the mod of a complex number so just skip all that.

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In retrospect, I feel like my time would have been much better spent studying group theory...

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diazona said:numbersall the time, but it's generally just arithmetic, complex conjugation, complex exponentials (like exp(i*x) = cos(x) + i*sin(x)), and Taylor series (occasionally Laurent series) of functions, usually real ones. None of which I needed a complex analysis course to understand.

In retrospect, I feel like my time would have been much better spent studying group theory...

did you do the residue theorem in that class?

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I think it depends on where you plan to go with physics and what area you wish to get into. There are some areas where it could be something that is very helpful and others where it is not needed.

I would say look into what you plan to be and see if the course would be relevant.

hope this helps.

~N~

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ice109 said:you're probably just using the complex expression of the Fourier series which isn't really complex analysis.

anyway having just finished my complex "variables" final, an applied complex analysis class, i can tell you that the only useful thing i got out of it was the calculus of residues and laurent series. so yea. skip that class and just learn how to use/do those two things. of course for both those things you'll need to understand things like analytic functions and the cauch riemann equations. we spent half a semester covering stupid things like how to take the mod of a complex number so just skip all that.

Good to know :) I actually saw residue theorem, Laurent series, and Cauchy-Riemann in a class that was called mathematical methods for physicists so if something like that is offered it might be more worthwhile. The class I took picked out what was deemed to be useful out of complex analysis while also getting other things such as tensor analysis. /shrug

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Lambduh said:Good to know :) I actually saw residue theorem, Laurent series, and Cauchy-Riemann in a class that was called mathematical methods for physicists so if something like that is offered it might be more worthwhile. The class I took picked out what was deemed to be useful out of complex analysis while also getting other things such as tensor analysis. /shrug

yea just look up indented paths and how to do trig integrals using the residue theorem and you're golden. there's some stuff in the back of my complex analysis book about conformal mappings but i have yet to check that out so i don't know if it's useful or not.

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loom91 said:

That's a fabulous analogy, and I now will be planning on adding complex analyses to my upcoming curriculum. Eventually. :)

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loom91 said:

what in the hell makes you say so?

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On the other hand, I have heard that Complex Analysis books have a lot of computation, even in the proofs. Spivak's Calculus introduces the very basics of complex analysis fairly nicely, yet his proof of the fundamental theorem of algebra looks horrible.

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1) The integral of a function over a closed curve is determined

2) A function takes on every value (except possibly one) infinitely often in any neighborhood of an essential singularity. (Piccard's Theorem)

If that's not beauty, I don't know what is.

And if you go through a full development of complex analysis then the Fundamental Theorem pops out as an immediate consequence of the brilliantly simple Louiville's Theorem: every non-constant function that is entire (differentiable everywhere on the complex plane) must be unbounded, a striking departure from the real case.

Molu

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Try Needham's Visual Complex Analysis. It may not be entirely rigorous, but it's very exciting.

Molu

Molu

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