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Conformal Mappings and Applications

In: Complex Analysis and Applications

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Listed:
  • Hemant Kumar Pathak

    (Pt. Ravishankar Shukla University, School of Studies in Mathematics)

Abstract

In the proceeding chapter, we have discussed some special types of bilinear transformations. As noted earlier that these transformations are the most powerful tools for transforming circular regions in the z-plane into circular regions or half-planes in the w-plane. In this chapter, we deal with more general situations in which we shall answer more abstract questions for determining whether and in what manner a given finite portion of an analytic surface could be represented on a portion of a plane (This well-posed problem was treated for the first time by Riemann (1826–1856) in his integral dissertation of Göttingen in 1851, which is indeed a decisive turning point in the history of Conformal Representation.).

Suggested Citation

  • Hemant Kumar Pathak, 2019. "Conformal Mappings and Applications," Springer Books, in: Complex Analysis and Applications, chapter 0, pages 559-623, Springer.
    • Handle: RePEc:spr:sprchp:978-981-13-9734-9_7
    DOI: 10.1007/978-981-13-9734-9_7
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