A concise textbook on complex analysis for undergraduate and graduate students, this book is written from the viewpoint of modern mathematics: the Bar {Partial}-equation, differential geometry, Lie groups, all the traditional material on complex analysis is included. Setting it apart from others, the book makes many statements and proofs of classical theorems in complex analysis simpler, shorter and more elegant: for example, the Mittag�Leffer theorem is proved using the Bar {Partial}-equation, and the Picard theorem is proved using the methods of differential geometry.

Contents:

• Calculus
• Cauchy Integral Theorem and Cauchy Integral Formula
• Theory of Series of Weierstrass
• Riemann Mapping Theorem
• Differential Geometry and Picard Theorem
• A First Taste of Function Theory of Several Complex Variables
• Elliptic Functions
• The Riemann Zeta-Function and the Prime Number Theorem

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