Real and Complex Analysis : Volume 1

Now in it second edition, this unique book develops the subject of analysis organically, by presenting techniques and concepts that apply more generally to functions of various types. This student textbook has been split into two volumes, with more flexibility added for instructors and an 800 additional exercises for students.

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.