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It seems to me that many schools each complex analysis in the applied math department. I notice that the article does mention applied math, but only down the list. Is it possible to include the reason why it is in AMa? Gah4 (talk) 06:42, 3 March 2021 (UTC)[reply]
It seems that there are classes that are more for theoretical math, and those more for engineers. I was thing about something like ACM95 at Caltech, which is required for most (or all) engineering degrees. I believe other schools have a similar course, often part of the AMa department. Gah4 (talk) 07:35, 24 June 2021 (UTC)[reply]
Gah4 Thank you for reply. I think complex analysis is related to AMa because it is related to vector analysis and harmonic functions, but I'm not ready to write it. And you can edit this article directly. Previously it was B-Class, but now it is C-Class. Therefore, there is nothing wrong with reorganizing the section.--SilverMatsu (talk) 08:56, 24 June 2021 (UTC)[reply]
(edit conflict)"Applied math" has at least four different meanings that are related but distinct. It may be the name of some courses or some university departements. This is not relevant for an encyclopedy, except for being mentioned in Applied mathematics. "Applied math" may refer to mathematics that are used outside mathematics. It appears that almost all parts of mathematics are implied (most items listed in APM95 do not belong to complex analysis), and this is why many of our articles have a section on applications, generally near to the end of the article. "Applied math" may refer to mathematics that are drived by applications. Finally "applied math" is often used as an alternate name for numerical analysis.
Yes. Well, it probably could apply to all mathematics used in sciences such as physics, and most engineering. For traditional reasons, it often doesn't. The AMa departments in schools that I know do things like computational fluid dynamics. Mostly numerical, so pure math people aren't so interested. I suspect, yes, it is sometimes used for numerical analysis but more often used for the less theoretical cases. And yes it is used for names of courses taught by people in the named department. So, yes, connected but distinct. Gah4 (talk) 09:39, 24 June 2021 (UTC)[reply]
The applied complex analysis, such as Laplace transforms used for EE filters, and contour integrals for a variety of computations, including inverse Laplace transforms. Also, some definite integrals that are hard to do other ways. Gah4 (talk) 09:39, 24 June 2021 (UTC)[reply]
In view of this, it would be useful to add a section "Applications" near to the end of the article, but this requires an editor with the needed competences and/or a reliable source on this. I do not see anything else to do. D.Lazard (talk) 09:21, 24 June 2021 (UTC)[reply]
I am considering to explain the relevance to Applied math by extending the exposition for Cauchy–Riemann conditions, mentioning the harmonic function, and then the Laplace equation, but I am not ready for reference and details. Next, we need to consider whether a holomorphic function actually exists, but for the open Riemann surface there is an Behnke–Stein theorem.--SilverMatsu (talk) 13:20, 24 June 2021 (UTC)[reply]
i happened to stumble upon this interesting exchange and i agree with the above: an applications section would definitely be handy. i also concur with D. Lazard that it would also require some proficiency in the area. it would not be fun, and would probably require tying the material from a few numerical analysis textbooks with the appropriate source for the "pure" variant. * dibbs out. maybe i'll lift someone else's edits and try to make it better. one suggestion i have is to motivate the section using the discussion of ordinary differential equations, particularly in terms of complex roots, move to fourier's (inferior) transform before discussing laplace. we have to start with DEs in my opinion. it will make everything easier. i never saw the use of complex analysis (being a huge fan of real analysis) until i started looking at the theory of differential equations. then i grew an appreciation for complex theory that is only starting to blossom, ten years after getting a reasonably-good grasp on real analysis theory. good chat here lads. "198.53.108.48 (talk) 19:04, 24 June 2021 (UTC)[reply]
Suggest to reorganize the section. First, I'm thinking of merging the holomorphic functions and complex functions sections. Next, I'm thinking of putting a section about the complex numbers (complex algebra) and the properties of the complex plane. I'm still thinking about the arrange of the sections, so I haven't thought about the details of the contents of the sections yet. --SilverMatsu (talk) 05:29, 20 October 2021 (UTC)[reply]
It would be good to provide a compressed summary of at least the main sections of an introductory complex analysis textbook, at least briefly describing the major ideas and results (the current "major results" section is much too compressed, and should be split into pieces). It might start with a quick explanation of complex numbers (describe how they add and multiply, and the negation, reciprocal, and complex conjugate), then talk about holomorphic functions, harmonic functions, power series, Laurent series, zeros and poles, line integrals and the residue theorem, analytic continuation, conformal mapping and the Riemann mapping theorem, elliptic functions, Riemann surfaces, uniformization, Fourier analysis, maybe the Riemann zeta function, .... It’s okay if some material is duplicated from other articles and it’s also okay if details and proofs are omitted and descriptions are more expository than formal/technical. It would be great to include as many figures as possible, because top-level articles like this are likely to have many nonspecialist readers. Disclaimer: I am not a mathematician. –jacobolus(t)16:36, 20 October 2021 (UTC)[reply]
Thank you for your reply. Now that we've started creating the list, please make update and additions. I agree that we need to add a figures. Thanks to @Nschloe: for creating the figures.--SilverMatsu (talk) 03:15, 21 October 2021 (UTC)[reply]
section list (draft)
History
Holomorphic functions
Cauchy–Riemann conditions
Cauchy's integral formula
Analytic functions (Power series (Laurent series))
Meromorphic function
Properties of singularity and residue (Especially isolated singularity)
