Complex analysis tutorials

[ZaidAlyafey]

I was planning to start contour integration on the advanced integration techniques tutorials . But I thought that it will be difficult to follow as I have to first introduce some concepts in complex analysis . So I asked myself why not starting tutorials on complex analysis then refer to them as references.

Do you think I should introduce the tutorials as brief explanation to only qualify the reader for Residue theory , or should it be so intensive that it covers everything ?

Feel free to give any suggestions .

 

[Jameson]

I think that you should keep the focus on integration so maybe you could briefly introduce a brief review/reference of topics that should be studied to use the integration methods you're going to introduce next. If there is interest or questions about how complex analysis and integration then it makes sense to elaborate in more depth, but it seems like there are already available textbooks on complex analysis for others to use. In general I feel that it's better to have fewer tutorials that are very, very in depth on lesser known topics than to have more tutorials on more topics.

That's my take on it, but I don't have a background in complex analysis at all so keep that in mind.

 

[ZaidAlyafey]

Thanks Jameson for the reply

I was hoping to make the tutorials as instructive as possible so the reader needn't read any other references . That seems to be working until now as all the topics I already discussed doesn't need any prior knowledge except elementary integration methods. I must be careful when I introduce the subject using contour integration because the topic is very important and there is some analysis involved before rushing to solve the integrals .This is clear from the examples I already gave [1] , [2] . I will try to introduce it differently and give the reader a clear overview of what he needs exactly before continuing threads . There are important theorems in complex analysis that I should explain myself so I make sure that the idea is clear . I will try to make the examples as instructive as possible .

 

[topsquark]

My two cents. Perhaps you should go ahead and do a brief introduction and then head into the "heavier" topics. Tell the readers to let you know what they need to understand the topic more fully? (That's pretty much how I did my Master's thesis.)

-Dan

 

[Jameson]

It is nice to have a tutorial that covers everything, but there is a point where the original topic can balloon into covering 15 other topics as well because and the whole thing gets out of control. That's my only point. I suppose you should just try writing some material on contour integration and background topics then see how it looks to everyone. We can give you our feedback then, which might be more useful than now since we are speaking kind of generally.