This book is an heirloom and a memorial. The first edition, dedicated “To My Epsilons,” appeared in the year that I (the youngest of my father's “little ones”) turned six years old. Now, many years later, my siblings being of a nonmathematical bent, the familial interest in the book resides in me. The most fitting tribute I can pay to my father's memory is to pass on a new edition of this monograph to the next generation of epsilons.

The principal change in this edition is the addition of a chapter on integration and some of its applications. This topic was deliberately omitted from previous editions, “reluctantly, because of the many technical details that are needed before one gets to the interesting results.” My father eventually decided that it would be acceptable and enjoyable to present some of the interesting results without all the technical details, on the principle that one need not understand the inner workings of the motor to appreciate a drive in the country. Chapter 3 is my reworking of a draft that my father left at his death. Besides revising this material, I have added most of the notes, exercises, and solutions for Chapter 3.