Kapak Resmi

Complex Analysis in One Variable and Riemann Surfaces

This textbook is intended for an introductory course in the theory of complex analysis and Riemann surfaces. A special feature includes the systematic treatment of complex analysis from the point of view of partial differential equations. The main goal is to study complex analysis in one variable us...

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Kaydedildi:
Detaylı Bibliyografya
Asıl Yazarlar: Shaw, Mei-Chi (Yazar), Stanton, Charles M. (Yazar)
Müşterek Yazar: SpringerLink (Online service)
Materyal Türü: Elektronik Ekitap
Dil:İngilizce
Baskı/Yayın Bilgisi: Cham : Springer Nature Switzerland : Imprint: Springer, 2025.
Edisyon:1st ed. 2025.
Seri Bilgileri:Graduate Texts in Mathematics, 305
Konular:
Functions of complex variables.
Differential equations.
Geometry, Differential.
Functions of a Complex Variable.
Differential Equations.
Differential Geometry.
Online Erişim:https://doi.org/10.1007/978-3-031-93642-5
Etiketler: Etiketle
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İçindekiler:
  • Preface
  • 1 Basic properties of holomorphic functions
  • 2 Complex integration
  • 3 Singularities and the residue theorem
  • 4 Holomorphic functions on simply connected domains
  • 5 Prescribing zeros and poles
  • 6 The inhomogeneous Cauchy-Riemann equation
  • 7 Riemann Surfaces
  • 8 Harmonic functions and the Dirichlet problem
  • 9 The Dirichlet problem: L^2 techniques
  • 10 Function theory on compact Riemann surfaces
  • 11 The uniformization theorem
  • 12 An introduction to several complex variables
  • A Compactness in function spaces
  • B Hilbert spaces
  • C Integral kernels and Fourier series
  • D Fourier transforms and the Rellich lemma
  • E Distributions and fundamental solutions
  • F Cohomology on a Riemann surface
  • Bibliography
  • Index.

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