New and updated content and features

• Updated and added numerous exercises throughout, with emphasis on the mid-level and more in the life science areas
• Many figures are reworked and many new ones have been added
• The discussion of conditional convergence has been moved to follow the Alternating Series Test
• Enhanced! The discussion defining differentiability for functions of several variables now includes more emphasis on linearization
• The authors show that the derivative along a path generalizes the single-variable chain rule
• More geometric insight is added to the presentation of the idea of multiple integrals and the meaning of the Jacobian in substitutions for their evaluations
• Surface integrals of vector fields are developed as generalizations of line integrals
• The authors have extended and clarified the discussion of the curl and divergence, and added new figures to help visualize their meanings

MyMathLab not included. Students, if MyMathLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN and course ID. MyMathLab should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. MyMathLab includes thousands of assignable algorithmic exercises, the complete eBook, tutorial videos, tools to personalize learning, and more. New features of the MyMathLab course for this edition include the following:

• Hundreds of new assignable exercises help you better meet student needs.
• More than 100 new tutorial videos (over 8 hours’ worth), created by experienced calculus professors, provide help to students beyond office hours. The creators of the videos wanted to avoid the sort of "cookbook" videos that are so prevalent on the Internet, but at the same time realize that students usually seek out videos when they are stuck on specific problems. So they do cover key examples, but in doing so, they address the conceptual underpinnings that are so important to student success in the course.
• Integrated Review tools address gaps in prerequisite skills that often impede success in the course. Students can use this content independently, or instructors can target individual student needs by using the built-in diagnostic quizzes and Personalized Homework. MyMathLab provides just-in-time help for skill gaps so that instructors can focus on teaching calculus.