Single Variable Calculus: Early Transcendentals 9th Edition

Book Preface

A great discovery solves a great problem but there is a grain of discovery in the solution  of any problem. Your problem may be modest; but if it challenges your curiosity and  brings into play your inventive faculties, and if you solve it by your own means, you may  experience the tension and enjoy the triumph of discovery.

george polya

The art of teaching, Mark Van Doren said, is the art of assisting discovery. In this Ninth  Edition, as in all of the preceding editions, we continue the tradition of writing a book  that, we hope, assists students in discovering calculus—both for its practical power and  its surprising beauty. We aim to convey to the student a sense of the utility of calculus as well as to promote development of technical ability. At the same time, we strive to give  some appreciation for the intrinsic beauty of the subject. Newton undoubtedly experienced a sense of triumph when he made his great discoveries. We want students to share  some of that excitement.

The emphasis is on understanding concepts. Nearly all calculus instructors agree that  conceptual understanding should be the ultimate goal of calculus instruction; to implement this goal we present fundamental topics graphically, numerically, algebraically,  and verbally, with an emphasis on the relationships between these different representations. Visualization, numerical and graphical experimentation, and verbal descriptions  can greatly facilitate conceptual understanding. Moreover, conceptual understanding and technical skill can go hand in hand, each reinforcing the other.

We are keenly aware that good teaching comes in different forms and that there  are different approaches to teaching and learning calculus, so the exposition and exercises are designed to accommodate different teaching and learning styles. The features  (including projects, extended exercises, principles of problem solving, and historical  insights) provide a variety of enhancements to a central core of fundamental concepts  and skills. Our aim is to provide instructors and their students with the tools they need to chart their own paths to discovering calculus.

Alternate Versions

The Stewart Calculus series includes several other calculus textbooks that might be  preferable for some instructors. Most of them also come in single variable and multivariable versions.
• Calculus, Ninth Edition, is similar to the present textbook except that the exponential, logarithmic, and inverse trigonometric functions are covered after the chapter  on integration.
• Essential Calculus, Second Edition, is a much briefer book (840 pages), though it  contains almost all of the topics in Calculus, Ninth Edition. The relative brevity is  achieved through briefer exposition of some topics and putting some features on the  website • Essential Calculus: Early Transcendentals, Second Edition, resembles Essential  Calculus, but the exponential, logarithmic, and inverse trigonometric functions are covered in Chapter 3.
• Calculus: Concepts and Contexts, Fourth Edition, emphasizes conceptual understanding even more strongly than this book. The coverage of topics is not encyclopedic and the material on transcendental functions and on parametric equations is woven throughout the book instead of being treated in separate chapters.
• Brief Applied Calculus is intended for students in business, the social sciences, and  the life sciences.
• Biocalculus: Calculus for the Life Sciences is intended to show students in the life  sciences how calculus relates to biology.
• Biocalculus: Calculus, Probability, and Statistics for the Life Sciences contains all  the content of Biocalculus: Calculus for the Life Sciences as well as three additional chapters covering probability and statistics.

What’s New in the Ninth Edition?

The overall structure of the text remains largely the same, but we have made many  improvements that are intended to make the Ninth Edition even more usable as a teaching tool for instructors and as a learning tool for students. The changes are a result of  conversations with our colleagues and students, suggestions from users and reviewers,  insights gained from our own experiences teaching from the book, and from the copious  notes that James Stewart entrusted to us about changes that he wanted us to consider for  the new edition. In all the changes, both small and large, we have retained the features  and tone that have contributed to the success of this book.
• More than 20% of the exercises are new: Basic exercises have been added, where appropriate, near the beginning of exercise sets. These exercises are intended to build student confidence and reinforce  understanding of the fundamental concepts of a section. (See, for instance, Exercises 7.3.1– 4, 9.1.1–5, 11.4.3–6.)
Some new exercises include graphs intended to encourage students to understand  how a graph facilitates the solution of a problem; these exercises complement  subsequent exercises in which students need to supply their own graph. (See
Exercises 6.2.1– 4 and 10.4.43– 46 as well as 53–54.) Some exercises have been structured in two stages, where part (a) asks for the  setup and part (b) is the evaluation. This allows students to check their answer  to part (a) before completing the problem. (See Exercises 6.1.1– 4 and 6.3.3– 4.)
Some challenging and extended exercises have been added toward the end of selected exercise sets (such as Exercises 6.2.87, 9.3.56, 11.2.79–81, and 11.9.47). Titles have been added to selected exercises when the exercise extends a concept  discussed in the section. (See, for example, Exercises 2.6.66 and 10.1.55–57.) Some of our favorite new exercises are 1.3.71, 3.4.99, 3.5.65, 4.5.55–58, 6.2.79,  6.5.18, and 10.5.69. In addition, Problem 14 in the Problems Plus following Chapter 6 is interesting and challenging.

• New examples have been added, and additional steps have been added to the solutions of some existing examples. (See, for instance, Example 2.7.5, Example 6.3.5,  and Example 10.1.5.)
• Several sections have been restructured and new subheads added to focus the  organization around key concepts. (Good illustrations of this are Sections 2.3, 11.1,  and 11.2.)
• Many new graphs and illustrations have been added, and existing ones updated, to  provide additional graphical insights into key concepts.
• A few new topics have been added and others expanded (within a section or in  extended exercises) that were requested by reviewers. (Examples include symmetric difference quotients in Exercise 2.7.60 and improper integrals of more than one  type in Exercises 7.8.65–68.)
• Derivatives of logarithmic functions and inverse trigonometric functions are now  covered in one section (3.6) that emphasizes the concept of the derivative of an  inverse function.
• Alternating series and absolute convergence are now covered in one section (11.5)