Real and Complex Analysis

ISBN-13: 9781584888062 / Angielski / Twarda / 2009 / 567 str.

Christopher Apelian;Steve Surace;Zuhair Nashed

Opis

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."

Providing the Material for a Two-Semester Course in Real Complex Analysis Taking a unique, unifying approach to the subject, this book presents the analysis of functions of real and complex variables together through a single, comprehensive point of view. It merges and relates relevant topics from both advanced calculus and complex analysis, which imparts a more cohesive understanding of analysis. This proven approach is consistent with the CUPM guidelines published in 2004 by the Mathematical Association of America that encourage the integration of related yet segregated topics in the undergraduate mathematics curriculum, which provides a clear understanding of the field.

Spis treści

The Spaces R, R^k, 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.

O autorze

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.