Calculus of Residues and Applications to Contour Integration

Hemant Kumar Pathak ()
Additional contact information
Hemant Kumar Pathak: Pt. Ravishankar Shukla University, School of Studies in Mathematics

Chapter Chapter 5 in Complex Analysis and Applications, 2019, pp 377-486 from Springer

Abstract: Abstract The inspiration behind this chapter is the desire to obtain possible values for the integrals $${\int _{C}} f(z)\, dz$$ , where f is analytic inside the closed curve C and on C, except for a inside C. If f has a removable singularity at a, then it is clear that the integral will be zero. If $$z =a$$ is a pole or an essential singularity, then the answer is not always zero, but can be found with little difficulty. In this chapter, we show the very surprising fact that Cauchy’s residue theorem yields a very elegant and simple method for evaluation of such integrals.

Date: 2019
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-13-9734-9_5

Ordering information: This item can be ordered from
http://www.springer.com/9789811397349

DOI: 10.1007/978-981-13-9734-9_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().