Christopher Apelian - Böcker

Presents Real & Complex Analysis Together Using a Unified ApproachA two-semester course in analysis at the advanced undergraduate or first-year graduate levelUnlike 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.

This unique book develops the subject of analysis organically, by presenting techniques and concepts that apply more generally to functions of various types. By considering these various function types together (real-valued functions of a single or several real variables, vector-valued functions of a single or several real variables, and complex functions), the student can better appreciate what is common to all of them, and what is distinctive to each. For the instructor, this approach also provides for certain pedagogical advantages. Like the first, the aim of this second edition of Real and Complex Analysis, Volume 1, is to benefit the student of analysis as best we can. Changes were made with the student in mind. The most evident change is one that we hope provides more flexibility to instructors, and more affordability to students. The new edition splits the text into two volumes, available individually or as a set. Other changes include clarifications and improvements suggested by readers. Exercises within each chapter have been thoroughly reviewed and reorganized, and partial solutions provided. Volume one has over 800 exercises in total, with more than 400 embedded exercises, and nearly the same number of end-of-chapter supplementary exercises. Also published by CRC Press: Real and Complex Analysis, Second Edition, Volume 2, Christopher Apelian and Steve Surace. Christopher Apelian completed a Ph.D. in mathematics in 1993 at New York University’s Courant Institute of Mathematical Sciences and then joined the Department of Mathematics and Computer Science at Drew University. He has published papers in the applications of probability and stochastic processes to the modeling of turbulent transport.Steve Surace joined Drew University’s Department of Mathematics and Computer Science in 1987 after earning his Ph.D. in mathematics from New York University’s Courant Institute. His mathematical interests include analysis, mathematical physics, and cosmology.