PREFACE TO THE

SECOND EDITION

       In this second edition, many changes have been made based on nine years of classroom experience. There are major revisions to the first six chapters and the Epilogue, and there is one completely new chapter, Chapter 14, on differential equations. In addition, the original Chapters 11 and 12 have been repackaged as three chapters: Chapter 11 on partial differentiation, Chapter 12 on multiple integration, and Chapter 13 on vector calculus.

        Chapter 1 has been shortened, and much of the theoretical material from the first edition has been moved to the Epilogue. The calculus of transcendental functions has been fully integrated into the course beginning in Chapter 2 on derivatives. Chapter 3 focuses on applications of the derivative. The material on setting up word problems and on related rates has been moved from the first two chapters to the beginning of Chapter 3. The theoretical results on continuous functions, including the Intermediate, Extreme, and Mean Value Theorems, have been collected in a single section at the end of Chapter 3. The development of the integral in Chapter 4 has been streamlined. The Trapezoidal Rule has been moved from Chapter 5 to Chapter 4, and a discussion of Simpson’s Rule has been added. The section on area between two curves has been moved from Chapter 6 to Chapter 4. Chapter 5 deals with limits, approximations, and analytic geometry. An extensive treatment of conic sections and a section on Newton’s method have been added. Chapter 6 begins with new material on finding a volume by integrating areas of cross sections.

Only minor changes and corrections have been made to Chapters 7 through 13. The new Chapter 14 gives a first introduction to differential equations, with emphasis on solving first and second order linear differential equations. In section 14.4, infinitesimals are used to give a simple proof that every differential equation y’=f(t,y), where f is continuous, has a solution. The proof of this fact is beyond the scope of a traditional elementary calculus course, but is within reach with infinitesimals.

I wish to thank all my friends and colleagues who have suggested corrections and improvements to the first edition of the book.

H.Jerome Keisler