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
The Spaces R, Rk, and C. Point-Set Topology. Limits and Convergence. Functions: Definitions and Limits. Functions: Continuity and Convergence. The Derivative. Real Integration. Complex Integration. Taylor Series, Laurent Series, and the Residue Calculus. Complex Functions as Mappings. Bibliography. Index.
Christopher Apelian is an associate professor and chair of the Department of Mathematics and Computer Science at Drew University. Dr. Apelian has published papers on the application of probability and stochastic processes to the modeling of turbulent transport.
Steve Surace is an associate professor in the Department of Mathematics and Computer Science at Drew University. Dr. Surace is also the Associate Director of the New Jersey Governor’s School in the Sciences held at Drew University every summer.