An Introduction to Mathematical Analysis (International Series in Pure and Applied Mathematics)

For students about to take their first mathematical analysis course, An Introduction to Mathematical Analysis, Second Edition, provides a rigorous, yet gentle treatment of the calculus of one real variable. The authors have taken care to present the material patiently, especially in the first few introductory chapters. The text encourages students to develop an aesthetic appreciation to the nature and role of the mathematical proof.
Coupling the gentle presentation with comprehensive coverage, the authors carefully motivate each discussion. The approach becomes more demanding as the text explores a range of topics from the early discussions on the reading and writing of mathematics to the treatment of sets of measure zero. The latter chapters contain a number of innovative and optional sections that provide elementary coverage of topics not usually covered in a book at this level.
This second edition features a completely redesigned format and a revised illustration program. The organization of the text has been changed so that the material on infinite series now precedes the chapter on Riemann integration. Many of the discussions have been streamlined and optional sections are starred, and can be omitted without loss of continuity.