Complex Analysis, an Introduction to the Theory of Analytic Functions of One Complex Variable by Lars V. Ahlfors (PDF)

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Excerpt from the Preface: The author’s ambition has been to write a text which is at once concise and rigorous, teachable and readable. Such a goal cannot be reached, it can only be approximated, and the author is aware of many shortcomings. No attempt has been made to make the book self-contained. On the contrary, a basic knowledge of real numbers and calculus, including the definition and properties of definite integrals, is taken for granted. Questions concerning limits and continuity are reviewed in connection with their application to complex numbers, and an effort is made not to rely on results which in elementary teaching are commonly derived in a sloppy or insufficient manner. The present author has wished to give the reader a solid foundation in classical complex-function theory by emphasizing the general principles on which it rests.

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