• 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.
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.
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.
Titles have been added to selected exercises when the exercise extends a concept discussed in the section.
• New examples have been added, and additional steps have been added to the solutions of some existing examples.
• Several sections have been restructured and new subheads added to focus the organization around key concepts.
• 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.
• New projects have been added and some existing projects have been updated.
• 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 (10.5).
• Conceptual Exercises
The most important way to foster conceptual understanding is through the problems that the instructor assigns. To that end we have included various types of problems. Some exercise sets begin with requests to explain the meanings of the basic concepts of the section and most exercise sets contain exercises designed to reinforce basic understanding. Other exercises test conceptual understanding through graphs or tables.
Many exercises provide a graph to aid in visualization. Another type of exercise uses verbal descriptions to gauge conceptual understanding.
We particularly value problems that combine and compare graphical, numerical, and algebraic approaches.
• Graded Exercise Sets
Each exercise set is carefully graded, progressing from basic conceptual exercises, to skill-development and graphical exercises, and then to more challenging exercises that often extend the concepts of the section, draw on concepts from previous sections, or involve applications or proofs.
• Real-World Data
Real-world data provide a tangible way to introduce, motivate, or illustrate the concepts of calculus. As a result, many of the examples and exercises deal with functions defined by such numerical data or graphs. These real-world data have been obtained by contacting companies and government agencies as well as researching on the Internet and in libraries.
One way of involving students and making them active learners is to have them work (perhaps in groups) on extended projects that give a feeling of substantial accomplishment when completed.
Applied Projects involve applications that are designed to appeal to the imagination of students.
Discovery Projects anticipate results to be discussed later or encourage discovery through pattern recognition. Other discovery projects explore aspects of geometry: tetrahedra, hyperspheres, and intersections of three cylinders.
JAMES STEWART was professor of mathematics at McMaster University and the University of Toronto for many years. James did graduate studies at Stanford University and the University of Toronto, and subsequently did research at the University of London. His research field was Harmonic Analysis and he also studied the connections between mathematics and music.
DANIEL CLEGG is professor of mathematics at Palomar College in Southern California. He did undergraduate studies at California State University, Fullerton and graduate studies at the University of California, Los Angeles (UCLA). Daniel is a consummate teacher; he has been teaching mathematics ever since he was a graduate student at UCLA.
SALEEM WATSON is professor emeritus of mathematics at California State University, Long Beach. He did undergraduate studies at Andrews University in Michigan and graduate studies at Dalhousie University and McMaster University. After completing a research fellowship at the University of Warsaw, he taught for several years at Penn State before joining the mathematics department at California State University, Long Beach.
JAMES STEWART 是麥克馬斯特大學和多倫多大學的數學教授，任教多年。James 在斯坦福大學和多倫多大學進行研究生學習，隨後在倫敦大學進行研究。他的研究領域是和諧分析，並且他也研究數學和音樂之間的聯繫。
DANIEL CLEGG 是加州南部帕洛瑪學院的數學教授。他在加州州立大學富勒頓分校進行本科學習，並在加州大學洛杉磯分校（UCLA）進行研究生學習。Daniel 是一位出色的教師；自從他在UCLA攻讀研究生以來，他一直在教授數學。
SALEEM WATSON 是加州長灘市加州州立大學的數學名譽教授。他在密歇根州安德魯斯大學進行本科學習，並在達爾豪西大學和麥克馬斯特大學進行研究生學習。在華沙大學完成研究研究員職位後，他在賓夕法尼亞州立大學教授了幾年，然後加入了加州長灘市加州州立大學的數學系。
I. Functions and Models
2. Limits and Derivatives
3. Differentiation Rules
4. Applications of Differentiation
6. Applications ofIntegration
7. Techniques of Integration
8. Further Applications of Integration
9. Parametric Equations and Polar Coordinates
10. Sequences, Series, and Power Series
11. Vectors and the Geometry of Space
12. Partial Derivatives
13. Multiple Integrals