"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"-- Read more...
Abstract:
Presents the analysis of functions of real and complex variables. This work relates relevant topics from both advanced calculus and complex analysis, which imparts a more cohesive understanding of analysis. Read more...
Author(s): Apelian, Christopher; Mathew, Akhil; Surace, Steve
Series: Chapman & Hall/CRC Pure and Applied Mathematics
Publisher: Chapman & Hall/CRC
Year: 2009
Language: English
Pages: 567
Tags: Математика;Математический анализ;
Content: 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