This book is intended for students familiar with the novice version of differential and integral calculus that emphasizes only the failure of manipulation and who are now looking for a closer study of basic concepts coupled with more creative use of information. This work is primarily aimed at students in mathematics, engineering and science who find themselves in transition from basic calculus to rigorous courses in analysis.

In addition, this book may also be of interest to those who are preparing to teach a course in calculus. Instead of exposing the reader to a surplus of premature abstractions that could easily degenerate into cavities, I felt that it was very useful to emphasize educational and motivational examples. The book contains many practical examples and many exercises with useful hints or solution in outlines.

For further training, interested readers may wish to consult a book by the author entitled Problems and Proposals in Analysis (New York: Marcel Deker, 1979). For the history of calculus I recommend the book by C.

B. Boer, Concepts of Calculus (New York: Dover, 1949)..