Calculus: Early Transcendentals 9th Edition
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.
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, Exercises 10.4.43– 46 as well as 53–54, 15.5.1–2, 15.6.9–12, 16.7.15 and 24, 16.8.9 and 13.)
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, 6.3.3– 4, 15.2.7–10.)
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, 10.1.55–57,
15.2.80 – 81.)
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, 10.5.69, 15.1.38, and 15.4.3– 4. In addition, Problem 14 in the Problems Plus following Chapter 6 and Problem 4 in the Problems Plus following Chapter 15 are 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, Example 10.1.5, Examples 14.8.1 and 14.8.4, and Example 16.3.4.)
• 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, 11.2, and 14.2.)
• 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 a subsection on torsion in Section 13.3, symmetric difference quotients in Exercise 2.7.60, and improper integrals of more than one type in Exercises 7.8.65–68.)
• New projects have been added and some existing projects have been updated. (For instance, see the Discovery Project following Section 12.2, The Shape of a Hanging Chain.)
• 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).
• The chapter on Second-Order Differential Equations, as well as the associated appendix section on complex numbers, has been moved to the website.
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|December 9, 2020|
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