本書序言

• 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). 

本書特色

• 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.
• Projects
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.