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Title page Abstract Copyright Preface CONTENTS Section I Fundamental Concepts Chapter 1. Numbers and Points § 1. Prerequisites § 2. The Plane and Sphere of Complex Numbers § 3. Point Sets and Sets of Numbers § 4. Paths, Regions, Continua Chapter 2. Functions of a Complex Variable § 5. The Concept of a Most General (Single-valued) Function of a Complex Variable § 6. Continuity and Differentiability § 7. The Cauchy-Riemann Differential Equations Section II Integral Theorems Chapter 3. The Integral op a Continuous Function § 8. Definition of the Definite Integral § 9. Existence Theorem for the Definite Integral § 10. Evaluation of Definite Integrals § 11. Elementary Integral Theorems Chapter 4. Cauchy's Integral Theorem § 12. Formulation of the Theorem § 13. Proof of the Fundamental Theorem § 14. Simple Consequences and Extensions Chapter 5. Cauchy's Integral Formulas § 15. The Fundamental Formula § 16. Integral Formulas for the Derivatives Section III Series and the Expansion of Analytic Functions in Series Chapter 6. Series with Variable Terms § 17. Domain of Convergence § 18. Uniform Convergence § 19. Uniformly Convergent Series of Analytic Functions Chapter 7. The Expansion of Ana

Who reads Theory of functions. Part 1?

Author

Knopp K.

Publisher

Dover

Published

1945

Language

EN

Category

nonfiction