Complex Analysis (Princeton Lectures in Analysis, No. 2)

By Elias M. Stein & Rami Shakarchi

Complex Analysis, Volume II of the acclaimed Princeton Lectures in Analysis, is a rigorous yet accessible introduction to the theory of complex variables. Written by Elias M. Stein and Rami Shakarchi, this text builds on real analysis foundations to develop the central ideas of complex function theory with clarity and depth.

Widely adopted in leading universities, the book connects analytic theory with applications in mathematics, physics, and engineering. It emphasizes conceptual understanding while maintaining the precision required for advanced study.

What This Book Does

This book develops the core principles of complex analysis, including holomorphic functions, contour integration, Cauchy’s theorem, residues, and conformal mappings. It bridges rigorous theory with practical insight and prepares readers for further study in analysis and applied mathematics.

Key Features

• Comprehensive introduction to complex variable theory
• Clear proofs supported by intuitive explanations
• Integrated problem sets suitable for coursework and self-study
• Strong connections to harmonic analysis and partial differential equations
• Part of the highly respected Princeton Lectures in Analysis series

Topics Covered

• Complex Numbers and Analytic Functions
• Holomorphic and Harmonic Functions
• Contour Integration and Cauchy’s Theorem
• Power Series and the Residue Theorem
• Conformal Mapping and Applications
• Analytic Continuation and the Gamma Function
• Boundary Value Problems and Harmonic Functions

A foundational text for mastering complex variables and analytic functions.
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