●The data in examples and exercises have been updated to be more timely.
●New examples have been added. And the solutions to some of the existing examples have been amplified.
●Three new projects have been added: For instance, in the project The Speedo LZR Racer it is explained that this suit reduces drag in the water and, as a result, many swimming records were broken. Students are asked why a small decrease in drag can have a big effect on performance.
●I have streamlined Chapter 13 (Multiple Integrals) by combining the first two sections so that iterated integrals are treated earlier.
●Many exercises in each chapter are new.
The most important way to foster conceptual understanding is through the problems that we assign. To that end I have devised various types of problems. Some exercise sets begin with requests to explain the meanings of the basic concepts of the section. Other exercises test conceptual understanding through graphs or tables.
Another type of exercise uses verbal description to test conceptual understanding. I 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 and skill-development problems to more challenging problems involving applications and proofs.
My assistants and I spent a great deal of time looking in libraries, contacting companies and government agencies, and searching the Internet for interesting real-world data to introduce, motivate, and illustrate the concepts of calculus. As a result, many of the examples and exercises deal with functions defined by such numerical data or graphs.
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. I have included four kinds of projects: 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.
1 Functions and Models
2 Limits and Derivatives
3 Differentiation Rules
4 Applications of Differentiation
6 Applications of Integration
7 Techniques of Integration
8 Further Applications of Integration
9 Parametric Equations and Polar Coordinates
10 Infinite Sequences and Series
11 Vectors, Vector Functions and the Geometry of Space
12 Partial Derivatives
13 Multiple Integrals