# Functions of One Complex Variable I

Springer Science & Business Media, Aug 24, 1978 - Mathematics - 317 pages
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This book is intended as a textbook for a first course in the theory of functions of one complex variable for students who are mathematically mature enough to understand and execute E - 8 arguments. The actual pre requisites for reading this book are quite minimal; not much more than a stiff course in basic calculus and a few facts about partial derivatives. The topics from advanced calculus that are used (e.g., Leibniz's rule for differ entiating under the integral sign) are proved in detail. Complex Variables is a subject which has something for all mathematicians. In addition to having applications to other parts of analysis, it can rightly claim to be an ancestor of many areas of mathematics (e.g., homotopy theory, manifolds). This view of Complex Analysis as "An Introduction to Mathe matics" has influenced the writing and selection of subject matter for this book. The other guiding principle followed is that all definitions, theorems, etc.

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Pl available this book as like as part II

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It is a great book. Clear writing and good exercise collection but a bit hard to follow.

### Contents

 Chapter I 1 Ho 7 Chapter II 11 Chapter III 30 Γ2 54 Chapter IV 58 G C is analytic 100 Chapter V 103
 Chapter VIII 195 Before stating Runges Theorem let us agree to say that 198 Chapter IX 210 G+ 212 T 242 γ 246 Chapter X 252 зи 256

 a 104 over it is not difficult to see that the 106 16 Determine the regions in which the functions f 112 for any closed rectifiable curve y not passing through a 122 Chapter VI 128 Thus 132 Chapter VII 142 for all z in K and n N But 172 equation will give that ƒ and I are everywhere identical 180
 applying Dinis Theorem Exercise VII16 Another involves 262 is harmonic in the right half piane and 0 272 Chapter XI 279 Chapter XII 292 Appendix A 303 Appendix B 307 1 L V AHLFORS Complex Analysis 311 Copyright

### References to this book

 Theory of Functions of a Complex Variable, Volumes 1-3Alekseï Ivanovitch MarkouchevitchNo preview available - 1977
 The Theory of Subnormal OperatorsJohn B. ConwayNo preview available - 1991
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