8. Sequences and Infinite Series 8.1 An overview 8.2 Sequences 8.3 Infinite series 8.4 The Divergence and Integral Tests 8.5 The Ratio, Root, and Comparison Tests 8.6 Alternating series   9. Power Series 9.1 Approximating functions with polynomials 9.2 Properties of Power series 9.3 Taylor series 9.4 Working with Taylor series   10. Parametric and Polar Curves 10.1 Parametric equations 10.2 Polar coordinates 10.3 Calculus in polar coordinates 10.4 Conic sections   11. Vectors and Vector-Valued Functions 11.1 Vectors in the plane 11.2 Vectors in three dimensions 11.3 Dot products 11.4 Cross products 11.5 Lines and curves in space 11.6 Calculus of vector-valued functions 11.7 Motion in space 11.8 Length of curves 11.9 Curvature and normal vectors   12. Functions of Several Variables 12.1 Planes and surfaces 12.2 Graphs and level curves 12.3 Limits and continuity 12.4 Partial derivatives 12.5 The Chain Rule 12.6 Directional derivatives and the gradient 12.7 Tangent planes and linear approximation 12.8 Maximum/minimum problems 12.9 Lagrange multipliers   13. Multiple Integration 13.1 Double integrals over rectangular regions 13.2 Double integrals over general regions 13.3 Double integrals in polar coordinates 13.4 Triple integrals 13.5 Triple integrals in cylindrical and spherical coordinates 13.6 Integrals for mass calculations 13.7 Change of variables in multiple integrals   14. Vector Calculus 14.1 Vector fields 14.2 Line integrals 14.3 Conservative vector fields 14.4 Green’s theorem 14.5 Divergence and curl 14.6 Surface integrals 14.6 Stokes’ theorem 14.8 Divergence theorem

A robust MyMathLab® course contains more than 7,000 assignable exercises, an eBook with 650 interactive figures, and built-in tutorials so students can get help when they need it. The MyMathLab course for the text features: More than 7,000 assignable exercises to provide you with the options you need to meet the needs of students. Most exercises can be algorithmically regenerated for unlimited practice. Learning aids include guided exercises, additional examples, and tutorial videos. You control how much help your students can get and when. 650 Interactive Figures in the eBook can be manipulated to shed light on key concepts. The figures are also ideal for in-class demonstrations. Interactive Figure Exercises provide a way for you to make the most of the Interactive Figures by including them in homework assignments. “Getting Ready for Calculus” chapter, with built-in diagnostic tests, identifies each student’s gaps in skills and provides personalized remediation for those skills that are lacking. NEW! Noteworthy changes to MyMathLab: Because many students now experience the text solely through the MyMathLab online homework system, many improvements have been made to the new Second Edition, including: NEW! The addition of: Hundreds of new algorithmic exercises that correspond to those in the text. To help determine which exercises to add, we analyzed data mined from students using the MyMathLab course from the first edition. Cumulative review exercises that provide an opportunity for students to get “mixed practice” with important skills such as finding derivatives and applying convergence tests. Setup & Solve exercises for key skills. These exercises provide support for students in their first attempts at new and important problems. More exercises that call for student manipulation and analysis of the Interactive Figures. Exercises that take advantage of the more sophisticated graphing functionality recently added to MyMathLab. A Conceptual Questions Library augments 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. Integrated Review MyLab Math 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 MyLab Math making it easier than ever to create your course. NEW! The requirement that students provide units for real-world exercises (e.g., meters/second). NEW! Answer-checking algorithms have been re-checked and refined where necessary. NEW! To address the growing use of video by students and instructors, we have greatly increased the number of instructional videos.   Reflects how students use a textbook— they generally start with the exercises and flip back to the narrative for help if they need it. Comprehensive exercise sets provide for a variety of student needs and are consistently structured and labeled to facilitate the creation of homework assignments. Review Questions check that students have a general conceptual understanding of the essential ideas from the section. Basic Skills exercises are linked to examples in the section so students get off to a good start with homework. Further Explorations exercises extend students’ abilities beyond the basics. Applications present practical and novel applications and models that use the ideas presented in the section. Additional Exercises challenge students to stretch their understanding by working through abstract exercises and proofs. NEW! 20% more exercises, including more mid-level exercises to enhance the pace of the book and give students more of a computational footing for the exercises that follow. When students flip back to the narrative for help with exercises, they find: Writing that reflects the voice of the instructor. Plentiful examples, each stepped-out in detail. Within examples, the steps are annotated in blue type to help students understand what took place in each step. Figures that are designed to teach rather than simply supplement the narrative. The figures are annotated to lead students through the key ideas, and rendered using the latest software for unmatched clarity and precision. Quick Check exercises punctuate the narrative at key points to test understanding of basic ideas and encourage students to read with pencil in hand.   Organization and presentation facilitates learning of key concepts, skills, and applications. Topics are introduced through concrete examples, geometric arguments, applications, and analogies rather than through abstract arguments. The authors appeal to students’ intuition and geometric instincts to make calculus natural and believable. The 650 Interactive Figures in the eBook provide a resource for instructors to help students visualize concepts where chalk or a marker falls short. The exercises that accompany the figures provide an opportunity for students to manipulate them as part of homework. Sequences and Series has been spread over two chapters to help clarify and pace it more effectively. Chapter 8, Sequences and Infinite Series, begins by providing a big picture with concrete examples of the difference between a sequence and a series followed by studying the properties and limits of sequences in addition to studying special infinite series and convergence tests. This chapter lays the groundwork for analyzing the absolute convergence for power series. Chapter 9, Power Series, begins with approximating with polynomials. Power series are introduced as a new way to define functions, building on one series by generating new series using composition, differentiation and integration. Taylor series are then covered and the motivation that precedes the section should make the topic more accessible. The authors chart a clear and uncluttered path through multivariable calculus. They separate cleanly vector-valued functions, functions of several variables, and vector calculus by placing them in separate chapters. This separation avoids common student errors, such as confusing the equation of a line and the equation of a plane in R3. The Instructor’s Resource Guide and Test Bank provides a wealth of instructional resources including Guided Projects, Lecture Support Notes with Key Concepts, Quick Quizzes for each section in the text, Chapter Reviews, Chapter Test Banks, Tips and Help for Interactive Figures, and Student Study Cards. Guided Projects, available for each chapter, require students to carry out extended calculations (e.g., finding the arc length of an ellipse), derive physical models (e.g., Kepler’s Laws), or explore related topics (e.g., numerical integration). The “guided” nature of the projects provides scaffolding to help students tackle these more involved problems.  

20% more exercises, including more mid-level exercises to enhance the pace of the book and give students more of a computational footing for the exercises that follow. A thorough, cover-to-cover polishing of the narrative in the second edition makes the presentation of material even more concise and lucid. An expanded section on tangent and principal normal vectors for vector curves now includes material on binormal vectors and TNB frames. Online chapters on both first- and second-order differential equations, in addition to the single robust survey section on first-order differential equations, have been added for schools requiring more expansive coverage of the topic. These new chapters can also be produced in print format. More fine-tuning of the content includes: The long introductory section in chapter 3 on derivatives is divided into two more digestible sections. In the Early Transcendentals version of the book, logarithmic and exponential functions are introduced in Chapter 1 and developed rigorously later in the book (Ch. 6). Instructors who cover the more theoretical material will find the coverage tightened up, along with a roadmap to make it easier for students to follow. Numerous new applied examples and exercises. Updating of all examples and exercises using real data to the most recent available values. Noteworthy changes to MyMathLab®: Because many students now experience the text solely through the MyMathLab online homework system, many improvements have been made to the new Second Edition, including: The addition of: Hundreds of new algorithmic exercises that correspond to those in the text. To help determine which exercises to add, we analyzed data mined from students using the MyMathLab course from the first edition. Cumulative review exercises that provide an opportunity for students to get “mixed practice” with important skills such as finding derivatives and applying convergence tests. Setup & Solve exercises for key skills. These exercises provide support for students in their first attempts at new and important problems. More exercises that call for student manipulation and analysis of the Interactive Figures. Exercises that take advantage of the more sophisticated graphing functionality recently added to MyMathLab. The requirement that students provide units for real-world exercises (e.g., meters/second). Answer-checking algorithms have been re-checked and refined where necessary. To address the growing use of video by students and instructors, we have greatly increased the number of instructional videos.