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Complex Analysis in One Variable

  • Raghavan Narasimhan
  • Yves Nievergelt

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Complex Analysis in One Variable

    1. Front Matter
      Pages 1-1
    2. Raghavan Narasimhan, Yves Nievergelt
      Pages 3-51
    3. Raghavan Narasimhan, Yves Nievergelt
      Pages 53-68
    4. Raghavan Narasimhan, Yves Nievergelt
      Pages 69-85
    5. Raghavan Narasimhan, Yves Nievergelt
      Pages 87-96
    6. Raghavan Narasimhan, Yves Nievergelt
      Pages 97-114
    7. Raghavan Narasimhan, Yves Nievergelt
      Pages 115-137
    8. Raghavan Narasimhan, Yves Nievergelt
      Pages 139-149
    9. Raghavan Narasimhan, Yves Nievergelt
      Pages 151-160
    10. Raghavan Narasimhan, Yves Nievergelt
      Pages 161-185
    11. Raghavan Narasimhan, Yves Nievergelt
      Pages 187-208
    12. Raghavan Narasimhan, Yves Nievergelt
      Pages 209-252
    13. Back Matter
      Pages 253-253
  3. Exercises

    1. Front Matter
      Pages 255-255
    2. Yves Nievergelt
      Pages 257-257
    3. Raghavan Narasimhan, Yves Nievergelt
      Pages 259-266
    4. Raghavan Narasimhan, Yves Nievergelt
      Pages 267-295
    5. Raghavan Narasimhan, Yves Nievergelt
      Pages 297-304
    6. Raghavan Narasimhan, Yves Nievergelt
      Pages 305-312
    7. Raghavan Narasimhan, Yves Nievergelt
      Pages 313-313
    8. Raghavan Narasimhan, Yves Nievergelt
      Pages 315-330
    9. Raghavan Narasimhan, Yves Nievergelt
      Pages 331-335
    10. Raghavan Narasimhan, Yves Nievergelt
      Pages 337-342
    11. Raghavan Narasimhan, Yves Nievergelt
      Pages 343-349
    12. Raghavan Narasimhan, Yves Nievergelt
      Pages 351-359
    13. Raghavan Narasimhan, Yves Nievergelt
      Pages 361-364
    14. Raghavan Narasimhan, Yves Nievergelt
      Pages 365-368
  4. Back Matter
    Pages 369-381

About this book

Introduction

This book presents complex analysis in one variable in the context of modern mathematics, with clear connections to several complex variables, de Rham theory, real analysis, and other branches of mathematics. Thus, covering spaces are used explicitly in dealing with Cauchy's theorem, real variable methods are illustrated in the Loman-Menchoff theorem and in the corona theorem, and the algebraic structure of the ring of holomorphic functions is studied.

Using the unique position of complex analysis, a field drawing on many disciplines, the book also illustrates powerful mathematical ideas and tools, and requires minimal background material. Cohomological methods are introduced, both in connection with the existence of primitives and in the study of meromorphic functionas on a compact Riemann surface. The proof of Picard's theorem given here illustrates the strong restrictions on holomorphic mappings imposed by curvature conditions.

New to this second edition, a collection of over 100 pages worth of exercises, problems, and examples gives students an opportunity to consolidate their command of complex analysis and its relations to other branches of mathematics, including advanced calculus, topology, and real applications.

Keywords

Meromorphic function Monodromy Residue theorem Riemann surfaces algebraic geometry complex analysis ksa real analysis

Authors and affiliations

  • Raghavan Narasimhan
    • 1
  • Yves Nievergelt
    • 2
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA
  2. 2.Department of MathematicsEastern Washington UniversityCheneyUSA

Bibliographic information

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