Foundations of analysis/ Steven G krantz

Includes bibliography and index

Number systems -- Sequences -- series of numbers -- Basic topology -- Limits and continuity of functions -- Differentiation of functions -- The Integral -- Sequences and series of functions -- Elementary transcendental functions

This book covers the basics of real analysis for a one- or two-semester course. In a straightforward and concise way, it helps students understand the key ideas and apply the theorems. The book’s accessible approach will appeal to a wide range of students and instructors.

Each section begins with a boxed introduction that familiarizes students with the upcoming topics and sets the stage for the work to be done. Each section ends with several questions that ask students to review what they have just learned. The text is also scattered with notes pointing out places where different pieces of terminology seem to conflict with each other or where different ideas appear not to fit together properly. In addition, many remarks throughout help put the material in perspective.

As with any real analysis text, exercises are powerful and effective learning tools. This book is no exception. Each chapter generally contains at least 50 exercises that build in difficulty, with an exercise set at the end of every section. This allows students to more easily link the exercises to the material in the section.