A Pathway to Complex Analysis

• Author: S. Kumaresan

• Publisher: Techno World

• Language: English

• Binding: Paperback

• Number of Pages: 300

About the Book:

• The book aims to provide a comprehensive introduction to Complex Analysis, bridging the gap between analysis, geometry, and topology.

• The curriculum has evolved significantly over the past five decades, and this book considers the improved background of students who now have exposure to real analysis, linear algebra, metric spaces, and topology.

• The salient features of this book include:

  • Careful treatment of arguments and logarithms.

  • Use of triangles and piecewise smooth paths instead of rectifiable paths.

  • Geometric treatments of Cauchy-Riemann (C-R) equations, winding numbers, and fractional linear transformations.

  • Geometric explanation of analytic continuation for beginners.

  • Emphasis on the conformal property of holomorphic functions using oriented angles.

  • Insightful remarks that offer a broader perspective and highlight the "big picture."

  • Focus on the Cauchy theory, particularly the existence of local primitives and the local power series expansion.

  • Clear explanations of how the properties of holomorphic functions are connected to power series.

• The book is designed to demystify complex analysis, especially for students who approach the subject with wonder, mystery, and awe. It aims to explain infinite differentiability of "analytic" functions and the concept of multivalued functions.