complicated evaluation, and mainly contour integrals and the residue idea have proved a totally effective tool in computing a massive class of real feature integrals which might be pretty difficult to compute if simplest inside the scope of real calculus. There are a exquisite many strategies designed for this cause, as an instance, both the selection of the complex variable characteristic and the choice of the ideal contour is critical to our fulfillment of computation.I want to study these techniques systematically, so I want recommendations for tutorials that cover them in a systematical way, the more inclusive the better. In a word, I want to learn as many those techniques as possible, so I think such a tutorial is a must.Ps: the tutorial I currently have at hand is Stein's Complex Analysis, it is good but covers too few exercises about such techniques.

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complicated evaluation, and mainly contour integrals and the residue idea have proved a totally effective tool in computing a massive class of real feature integrals which might be pretty difficult to compute if simplest inside the scope of real calculus. There are a exquisite many strategies designed for this cause, as an instance, both the selection of the complex variable characteristic and the choice of the ideal contour is critical to our fulfillment of computation.I want to study these techniques systematically, so I want recommendations for tutorials that cover them in a systematical way, the more inclusive the better. In a word, I want to learn as many those techniques as possible, so I think such a tutorial is a must.Ps: the tutorial I currently have at hand is Stein&#039;s Complex Analysis, it is good but covers too few exercises about such techniques.

Conner Singleton · Accepted Answer

The most comprehensive treatment of residue-based techniques that I know is the two volume set:The Cauchy method of residues: theory and applications by Mitrinović and Kečkić, Dordrecht, 1984 (ISBN: 9027716234).The Cauchy method of residues: theory and applications, Vol. 2 by the same authors, and publisher. This one published in 1993 (ISBN: 0792323114.)Amazon carries a one-volume book by the same authors and with a very similar title, published in 2001 by Kluwer, but I haven&#039;t seen that exact version.These books cover more or less every imaginable (and many unimaginable) application of residues.

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