Basic calculus Preface (second edition)

Preface to

Second Edition

In this second edition, please changes have been made based on nine yearsof classroom experience. There are major revisions to the first sixchapters
And the epilogue, and there is one completely new chapter, chapter 14, on differential equations. in addition, the originalchapters 11 and 12 have been repackaged as three chapters: Chapter 11on partial differentiation, chapter 12 on multiple integration, andchapter
13 on vector calculus.

Chapter1 has been shortened, and much of the theoretical material from thefirst edition has been moved to the epilogue. The calculus oftranscendental
Functions has been fully integrated into the coursebeginning in Chapter 2 on derivatives. chapter 3 focuses onapplications of the derivative. the material on setting up wordproblems and on related rates has been moved from the first twochapters to the beginning
Of Chapter 3. the theoretical results oncontinuous functions, including the intermediate, extreme, and meanvalue theorems, have been collected in a single section at the end ofChapter 3. the development of the integral in Chapter 4 has beenstreamlined. the
Trapezoidal Rule has been moved from chapter 5 tochapter 4, and a discussion of Simpson's rule has been added. thesection on area between two curves has been moved from chapter 6 tochapter 4. chapter 5 deals with limits, approximations, and analyticgeometry.
An extensive treatment of conic sections and a section onnewton's method have been added. Chapter 6 begins with new materiron finding a volume by integrating areas of cross sections.

Onlyminor changes and corrections have been made to Chapters 7 through13. the new Chapter 14 gives a first introduction to differentialequations,
With emphasis on solving first and second order lineardifferential equations. In section 14.4, infinitesimals are used togive a simple proof that every Differential Equation
Y' = f (t, Y), WhereFIs continuous, has a solution. The proof of this factis beyond the scope of a traditional elementary calculus course, butis within reach with infinitesimals.

Iwish to thank all my friends and colleagues who have suggestedcorrections and improvements to the first edition of the book.

H. jeromekeisler