Real and Complex Analysis

Presents Real & Complex Analysis Together Using a Unified Approach

A two-semester course in analysis at the advanced undergraduate or first-year graduate level

Unlike other undergraduate-level texts, Real and Complex Analysis develops both the real and complex theory together. It takes a unified, elegant approach to the theory that is consistent with the recommendations of the MAA’s 2004 Curriculum Guide.

By presenting real and complex analysis together, the authors illustrate the connections and differences between these two branches of analysis right from the beginning. This combined development also allows for a more streamlined approach to real and complex function theory. Enhanced by more than 1,000 exercises, the text covers all the essential topics usually found in separate treatments of real analysis and complex analysis. Ancillary materials are available on the book’s website.

This book offers a unique, comprehensive presentation of both real and complex analysis. Consequently, students will no longer have to use two separate textbooks—one for real function theory and one for complex function theory.

Table of Contents

Chapter 1: THE SPACES R,Rk, AND C
Chapter 2: POINT-SET TOPOLOGY
Chapter 3: LIMITS AND CONVERGENCE
Chapter 4: FUNCTIONS: DEFINITIONS AND LIMITS
Chapter 5: FUNCTIONS: CONTINUITY ANDCONVERGENCE
Chapter 6: THE DERIVATIVE
Chapter 7: REAL INTEGRATION
Chapter 8: COMPLEX INTEGRATION
Chapter 9: TAYLOR SERIES, LAURENT SERIES, ANDTHE RESIDUE CALCULUS
Chapter 10: COMPLEX FUNCTIONS AS MAPPINGS