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A Primer of Real Analytic Functions

  • Steven G. Krantz
  • Harold R. Parks

Part of the Birkhäuser Advanced Texts book series (BAT)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Steven G. Krantz, Harold R. Parks
    Pages 1-23
  3. Steven G. Krantz, Harold R. Parks
    Pages 25-66
  4. Steven G. Krantz, Harold R. Parks
    Pages 67-81
  5. Steven G. Krantz, Harold R. Parks
    Pages 83-113
  6. Steven G. Krantz, Harold R. Parks
    Pages 115-149
  7. Steven G. Krantz, Harold R. Parks
    Pages 151-186
  8. Back Matter
    Pages 187-209

About this book

Introduction

It is a pleasure and a privilege to write this new edition of A Primer 0/ Real Ana­ lytic Functions. The theory of real analytic functions is the wellspring of mathe­ matical analysis. It is remarkable that this is the first book on the subject, and we want to keep it up to date and as correct as possible. With these thoughts in mind, we have utilized helpful remarks and criticisms from many readers and have thereby made numerous emendations. We have also added material. There is a now a treatment of the Weierstrass preparation theorem, a new argument to establish Hensel's lemma and Puiseux's theorem, a new treat­ ment of Faa di Bruno's forrnula, a thorough discussion of topologies on spaces of real analytic functions, and a second independent argument for the implicit func­ tion theorem. We trust that these new topics will make the book more complete, and hence a more useful reference. It is a pleasure to thank our editor, Ann Kostant of Birkhäuser Boston, for mak­ ing the publishing process as smooth and trouble-free as possible. We are grateful for useful communications from the readers of our first edition, and we look for­ ward to further constructive feedback.

Keywords

Algebraic Geometry Complex Analysis: one Variable Implicit function Partial Differential Equations Real Analysis calculus differential equation partial differential equation

Authors and affiliations

  • Steven G. Krantz
    • 1
  • Harold R. Parks
    • 2
  1. 1.Department of MathematicsWashington UniversitySt. LouisUSA
  2. 2.Department of MathematicsOregon State UniversityCorvallisUSA

Bibliographic information

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