Features and Benefits

About the Book

Teach calculus the way you want to teach it, and at a level that prepares students for their STEM majors

• New co-author Chris Heil (Georgia Institute of Technology) and co-author Joel Hass continue Thomas’ tradition of developing students’ mathematical maturity and proficiency, going beyond memorizing formulas and routine procedures, and showing students how to generalize key concepts once they are introduced.
• The authors are careful to present key topics, such as the definition of the derivative, both informally and formally. The distinction between the two is clearly stated as each is developed, including an explanation as to why a formal definition is needed. Ideas are introduced with examples and intuitive explanations that are then generalized so that students are not overwhelmed by abstraction.
• Results are both carefully stated and proved throughout the book, and proofs are clearly explained and motivated. Students and instructors who proceed through the formal material will find it as carefully presented and explained as the informal development. If the instructor decides to downplay formality at any stage, it will not cause problems with later developments in the text.
• A flexible table of contents divides topics into manageable sections, allowing instructors to tailor their course to meet the specific needs of their students.
• Complete and precise multivariable coverage enhances the connections of multivariable ideas with their single-variable analogues studied earlier in the book.

Assess student understanding of key concepts and skills through a wide range of time-tested exercises

• Strong exercise sets feature a great breadth of problems–progressing from skills problems to applied and theoretical problems–to encourage students to think about and practice the concepts until they achieve mastery. In the 14th Edition, the authors added new exercises throughout, many geometric in nature.
• Writing exercises placed throughout the text ask students to explore and explain a variety of calculus concepts and applications. In addition, the end of each chapter contains a list of questions for students to review and summarize what they have learned. Many of these exercises make good writing assignments.
• Technology exercises (marked with a T) are included in each section, asking students to use the calculator or computer when solving the problems. In addition, Computer Explorations give the option of assigning exercises that require a computer algebra system (CAS, such as Maple or Mathematica).

Support a complete understanding of calculus for students at varying levels

• Each major topic is developed with both simple and more advanced examples to give the basic ideas and illustrate deeper concepts.
• UPDATED! Figures are conceived and rendered to provide insight for students and support conceptual reasoning. In the 14th Edition, new figures are added to enhance understanding and graphics are revised throughout to emphasize clear visualization.
• ENHANCED! Annotations within examples (shown in blue type) guide students through the problem solution and emphasize that each step in a mathematical argument is rigorously justified. For the 14th Edition, many more annotations were added.
• End-of-chapter materials include review questions, practice exercises covering the entire chapter, and a series of Additional and Advanced Exercises with more challenging or synthesizing problems.
• A complete suite of instructor and student supplements saves class preparation time for instructors and improves students’ learning.

Also available with MyMathLab® for School

MyMathLab® for School is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. A full suite of Interactive Figures have been added to the accompanying MyMathLab for School course to further support teaching and learning. Enhanced Sample Assignments include just-in-time prerequisite review, help keep skills fresh with distributed practice of key concepts, and provide opportunities to work exercises without learning aids to help students develop confidence in their ability to solve problems independently.

Engage students with the power of calculus through a variety of multimedia resources

• NEW! A full suite of Interactive Figures has been added to support teaching and learning. The figures illustrate key concepts and allow manipulation. They have been designed to be used in lecture as well as by students independently. Videos that use the Interactive Figures to explain key concepts are included. The figures are editable using the freely available GeoGebra software. The figures were created by Marc Renault (Shippensburg University), Steve Phelps (University of Cincinnati), Kevin Hopkins (Southwest Baptist University), and Tim Brzezinski (Berlin High School, CT).
• UPDATED! Instructional videos: Hundreds of videos are available as learning aids within exercises and for self-study. The Guide to Video-Based Assignments makes it easy to assign videos for homework by showing which MyMathLab for School exercises correspond to each video.
• The complete eText is available to students through their MyMathLab for School courses for the lifetime of the edition, giving students unlimited access to the eText within any course using that edition of the textbook.

Assess student understanding of concepts and skills through a wide range of exercises

• Exercises with immediate feedback–over 8080 assignable exercises for this text regenerate algorithmically to give students unlimited opportunity for practice and mastery. MyMathLab for School provides helpful feedback when students enter incorrect answers and includes optional learning aids including Help Me Solve This, View an Example, videos, and an eText.
• NEW! Setup & Solve exercises require students to first describe how they will set up and approach the problem. This reinforces conceptual understanding of the process applied in approaching the problem, promotes long term retention of the skill and mirrors what students will be expected to do on a test.
• NEW! Additional Conceptual Questions augment the text exercises to focus on deeper, theoretical understanding of the key concepts in calculus. These questions were written by faculty at Cornell University under an NSF grant and are also assignable through Learning Catalytics.
• NEW! Enhanced Sample Assignments are crafted to maximize student performance in the course. These section-level assignments include: (a) personalized, just-in-time prerequisite review exercises; (b) systematic distributed practice of key concepts (such as the Chain Rule) in order to help keep skills fresh, and (c) periodic removal of learning aids to help students develop confidence in their ability to solve problems independently.
• NEW! Integrated Review MyMathLab for School courses provide a full suite of supporting resources for the main course content plus additional assignments and study aids for students who will benefit from remediation. Assignments for the Integrated Review content are preassigned in MyMathLab for School, making it easier than ever to create your course.
• Learning Catalytics™ helps instructors generate class discussion, customize lectures, and promote peer-to-peer learning with real-time analytics. As a student response tool, Learning Catalytics uses students’ smartphones, tablets, or laptops to engage them in more interactive tasks and thinking. Learning Catalytics allows you to
  • Help your students develop critical thinking skills.
  • Monitor responses to find out where your students are struggling.
  • Rely on real-time data to adjust your teaching strategy.
  • Automatically group students for discussion, teamwork, and peer-to-peer learning.