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. The relative brevity is achieved through briefer exposition of some topics and putting some features on the website.
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. 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.
These exercises are intended to build student confidence and reinforce understanding of the fundamental concepts of a section. See, for instance, Exercises 7. 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. 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. Some challenging and extended exercises have been added toward the end of selected exercise sets such as Exercises 6.
They require a minimum of computation and are answered by filling in the blanks. Focus on Concepts Exercises Each exercise set contains a clearly identified group of problems that focus on the main ideas of the section. Technology Exercises Most sections include exercises that are designed to be solved using either a graphing calculator or a computer algebra system such as Mathematica, Maple, or the open source program Sage.
These exercises are marked with an icon for easy identification. This theme is carried through in the examples and exercises. Career Preparation This text is written at a mathematical level that will prepare students for a wide variety of careers that require a sound mathematics background, including engineering, the various sciences, and business. Trigonometry Review Deficiencies in trigonometry plague many students, so we have included a substantial trigonometry review in Appendix B.
Appendix on Polynomial Equations Because many calculus students are weak in solving polynomial equations, we have included an appendix Appendix C that reviews the Factor Theorem, the Remainder Theorem, and procedures for finding rational roots.
The chapter emphasizes general methods and the role of technology rather than specific tricks for evaluating complicated or obscure integrals.
Historical Notes The biographies and historical notes have been a hallmark of this text from its first edition and have been maintained. Margin Notes and Warnings These appear in the margins throughout the text to clarify or expand on the text exposition or to alert the reader to some pitfall.
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