Calculus: Single Variable 6th Edition

Book Preface

Calculus is one of the greatest achievements of the human intellect. Inspired by problems in astronomy, Newton and Leibniz developed the ideas of calculus 300 years ago. Since then, each century has demonstrated the power of calculus to illuminate questions in mathematics, the physical sciences, engineering, and the social and biological sciences.

Calculus has been so successful both because its central theme—change—is pivotal to an analysis of the natural world and because of its extraordinary power to reduce complicated problems to simple procedures. Therein lies the danger in teaching calculus: it is possible to teach the subject as nothing but procedures— thereby losing sight of both the mathematics and of its practical value. This edition of Calculus continues our effort to promote courses in which understanding and computation reinforce each other.

Mathematical Thinking Supported by Theory and Modeling

The first stage in the development of mathematical thinking is the acquisition of a clear intuitive picture of the central ideas. In the next stage, the student learns to reason with the intuitive ideas in plain English. After this foundation has been laid, there is a choice of direction. All students benefit from both theory and modeling, but the balance may differ for different groups. Some students, such as mathematics majors, may prefer more theory, while othersmay prefermoremodeling. For instructors wishing to emphasize the connection between calculus and other fields, the text includes:

• A variety of problems from the physical sciences and engineering.
• Examples from the biological sciences and economics.
• Models from the health sciences and of population growth.
• New problems on sustainability.
• New case studies on medicine by David E. Sloane, MD.

Origin of the Text

From the beginning, this textbook grew out of a community of mathematics instructors eager to find effective ways for students to learn calculus. This Sixth Edition of Calculus reflects the many voices of users at research universities, four-year colleges, community colleges, and secondary schools. Their input and that of our partner disciplines, engineering and the natural and social sciences, continue to shape our work.