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Calculus: Single and Multivariable, 6th Edition


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Calculus: Single and Multivariable, 6th Edition continues the effort to promote courses in which understanding and computation reinforce each other. The 6th Edition reflects the many voices of users at research universities, four-year colleges, community colleges, and secondary schools. This new edition has been streamlined to create a flexible approach to both theory and modeling. The text includes a variety of problems and examples from the physical, health, and biological sciences, engineering and economics; emphasizing the connection between calculus and other fields. In addition, new problems on the mathematics of sustainability and new case studies on calculus in medicine by David E. Sloane, MD have been added.


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1. Introduction

1.1 Some Basic Mathematical Models; Direction Fields

  • 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.
  • Updated Data and Models: For example, Section 11.7 follows the current debate on Peak Oil Production, underscoring the importance of mathematics in understanding the world’s economic and social? problems.
  • Drill Exercises build student skill and confidence.
  • Online Problems available in WileyPLUS or WeBWorK, for example. Many problems are randomized,? providing students with expanded opportunities for practice with immediate feedback.
  • Projects at the end of each chapter provide opportunities for a sustained investigation, often using skills from different parts of the course.
  • 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.
  • Class Worksheets allow instructors to engage students in individual or group class-work. Samples are available in the Instructor’s Manual, and all are on the web at 


  • Innovative and engaging problems. Under the approach 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.
  • A Flexible Approach to Technology: Adaptable to courses having various levels of computer involvement, ranging from little or none to intensive. The book does not require any specific software or technology, though it has been used successfully with graphing calculators, graphing software, and computer algebra systems.
  • Applied Problems for instructors wishing to emphasize the connection between calculus and other fields.