A Primer of Real Analytic Functions

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Springer Science & Business Media, Jul 1, 2002 - Mathematics - 205 pages
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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.
  

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Contents

Elementary Properties
1
Multivariable Calculus of Real Analytic Functions
25
Classical Topics
67
Some Questions of Hard Analysis
83
Results Motivated by Partial Differential Equations
115
Topics in Geometry
151
Bibliography
187
Index
203
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About the author (2002)

Steven Krantz, Ph.D., is Chairman of the Mathematics Department at Washington University in St. Louis. An award-winning teacher and author, Dr. Krantz has written more than 45 books on mathematics, including "Calculus Demystified," another popular title in this series. He lives in St. Louis, Missouri.