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Hi, I am interested in taking a complex analysis course. How useful is it to the physical sciences?
you're probably just using the complex expression of the fourier series which isn't really complex analysis.I spend most of my time with electronics and lasers but i end up using complex analysis in some way all the time. Anything that can be described via a sine wave (harmonic motion) can also be expressed as a complex function, this happens quite often for me.
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.
did you do the residue theorem in that class?I'm finishing up my first year of graduate school in physics. I took one course in complex analysis as an undergrad, and to be honest, I don't think anything I learned in that class has ever been useful to me. People keep saying complex analysis is incredibly useful in physics but I'm still waiting to see evidence of that. Sure, I use complex numbers all 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...
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. /shrugyou'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.
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.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
That's a fabulous analogy, and I now will be planning on adding complex analyses to my upcoming curriculum. Eventually. :)I don't know how useful it is in "doing" physics, but I think learning complex analysis deeply fills a hole that every human being has in their heart after taking just real calculus, whether they know it or not. It's like standing in front of the Louvre and deciding whether to go in: it's not a decision that should be taken on the basis of material usefulness.
what in the hell makes you say so?I don't know how useful it is in "doing" physics, but I think learning complex analysis deeply fills a hole that every human being has in their heart after taking just real calculus, whether they know it or not. It's like standing in front of the Louvre and deciding whether to go in: it's not a decision that should be taken on the basis of material usefulness.