Contents
Preface xiii
Chapter 1. Selected Problems in One Complex Variable 1
§1.1. Preliminaries 2
§1.2. A Simple Problem 2
§1.3. Partitions of Unity 4
§1.4. The Cauchy-Riemann Equations 7
§1.5. The Proof of Proposition 1.2.2 10
§1.6. The Mittag-Leffler and Weierstrass Theorems 12
§1.7. Conclusions and Comments 16
Exercises 18
Chapter 2. Holomorphic Functions of Several Variables 23
§2.1. Cauchy's Formula and Power Series Expansions 23
§2.2. Hartog's Theorem 26
§2.3. The Cauchy-Riemann Equations 29
§2.4. Convergence Theorems 29
§2.5. Domains of Holomorphy 31
Exercises 35
Chapter 3. Local Rings and Varieties 37
§3.1. Rings of Germs of Holomorphic Functions 38
53.2. Hilbert's Basis Theorem 39
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