Real and Complex Analysis

This text presents real and complex integration theory, as well as mapping properties of complex functions from the complex plane to itself. Comprising the second volume to the second edition of Real and Complex Analysis, this work completes the development, begun in Volume 1, of real and complex functions and their properties. The two volumes together present a unique, yet elegant and approachable treatment of analysis. Like the first volume, Volume 2 was written with the student in mind. Containing more examples and a more thorough treatment of mappings than the first edition, the text offers over 300 exercises. It provides hints and solutions to all odd-numbered embedded problems, and continues the authors’ philosophy of exploring real and complex functions side-by-side, as in Volume 1. Chapter 1 rigorously develops the Riemann integral and its properties, while Chapter 2 is devoted to the rich and rewarding theory of complex integration. Chapter 3 introduces power series, Taylor series, and Laurent series, including the fundamentals of the residue calculus for computing both real and complex integrals. Finally, the fourth chapter explores complex functions as mappings of the complex plane. Intended for advanced undergraduates who have completed a college-level calculus sequence and a first course in proof techniques, it is also well-suited for a first-year graduate course in analysis.