Introduction to Real Analysis

Description

This classic textbook has been used successfully by instructors and students for nearly three decades. This timely new edition offers minimal yet notable changes while retaining all the elements, presentation, and accessible exposition of previous editions. A list of updates is found in the Preface to this edition. This text is based on the author’s experience in teaching graduate courses and the minimal requirements for successful graduate study. The text is understandable to the typical student enrolled in the course, taking into consideration the variations in abilities, background, and motivation. Chapters one through six have been written to be accessible to the average student, while at the same time challenging the more talented student through the exercises. Chapters seven through ten assume the students have achieved some level of expertise in the subject. In these chapters, the theorems, examples, and exercises require greater sophistication and mathematical maturity for full understanding. Contents Preface to the Third Edition Preface to the First Edition To the Student Acknowledgments 1 The Real Numbers 2 Topology of the Real Line 3 Sequences of Real Numbers 4 Limits and Continuity 5 Differentiation 6 Integration 7 Series of Real Numbers 8 Sequences and Series of Functions 9 Fourier Series 10 Lebesgue Measure and Integration Bibliography Hints and Solutions Index