Calculus: Single and Multivariable 6th Edition + Solutions Manual

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 others may prefer more modeling. 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.

Active Learning: Good Problems
As instructors ourselves, we know that interactive classrooms and well-crafted problems promote student learning. Since its inception, the hallmark of our text has been its innovative and engaging problems. These problems probe student understanding in ways often taken for granted. Praised for their creativity and variety, the influence of these problems has extended far beyond the users of our textbook.

The Sixth Edition continues this tradition. Under our approach, which we called the “Rule of Four,” ideas are presented graphically, numerically, symbolically, and verbally, thereby encouraging students with a variety of learning styles to expand their knowledge. This edition expands the types of problems available:
• New Strengthen Your Understanding problems at the end of every section. These problems ask students to reflect on what they have learned by deciding “What is wrong?” with a statement and to “Give an example” of an idea.
• ConcepTests promote active learning in the classroom. These can be used with or without clickers (personal response systems), and have been shown to dramatically improve student learning. Available in a book or on the web at www.wiley.com/college/hughes-hallett.