Calculus Early Transcendentals Combined (9th edition)

Book Preface

This ninth edition of Calculus maintains those aspects of previous editions that have led to the series’ success—we continue to strive for student comprehension without sacrificing mathematical accuracy, and the exercise sets are carefully constructed to avoid unhappy surprises that can derail a calculus class. However, this edition also has many new features that we hope will attract new users and also motivate past users to take a fresh look at our work. We had two main goals for this edition:

• To make those adjustments to the order and content that would align the text more precisely with the most widely followed calculus outlines.

• To add new elements to the text that would provide a wider range of teaching and learning tools.

All of the changes were carefully reviewed by an advisory committee of outstanding teachers comprised of both users and nonusers of the previous edition. The charge of this committee was to ensure that all changes did not alter those aspects of the text that attracted users of the eighth edition and at the same time provide freshness to the new edition that would attract new users. Some of the more substantive changes are described below.

NEW FEATURES IN THIS EDITION

Also, Section 14.4 (Surface Area; Parametric Surfaces) has been reorganized so surfaces of the form z = f (x, y) are discussed before surfaces defined parametrically.

Differential Equations Reorganized We reordered and revised the chapter on differential equations so that instructors who cover only separable equations can do so without a forced diversion into general first-order equations and other unrelated topics. This chapter can be skipped entirely by those who do not cover differential equations at all in calculus.

New 2D Discussion of Centroids and Center of Gravity In the eighth edition and earlier, centroids and center of gravity were covered only in three dimensions. In this edition we added a new section on that topic in Chapter 6 (Applications of the Definite Integral), so centroids and center of gravity can now be studied in two dimensions, as is common in many calculus courses.

Related Rates and Local Linearity Reorganized The sections on related rates and local linearity were moved to follow the sections on implicit differentiation and logarithmic, exponential, and inverse trigonometric functions, thereby making a richer variety of techniques and functions available to study related rates and local linearity.

Rectilinear Motion Reorganized The more technical aspects of rectilinear motion that were discussed in the introductory discussion of derivatives in the eighth edition have been deferred so as not to distract from the primary task of developing the notion of the derivative. This also provides a less fragmented development of rectilinear motion.

Other Reorganization The section Graphing Functions Using Calculators and Computer Algebra Systems, which appeared in the text body of the eighth edition, is now a text appendix (Appendix A), and the sections Mathematical Models and Second-Order Linear Homogeneous Differential Equations are now posted on theWeb site that supports the text.