9. Sequences and Infinite Series 9.1 An overview 9.2 Sequences 9.3 Infinite series 9.4 The Divergence and Integral Tests 9.5 The Ratio, Root, and Comparison Tests 9.6 Alternating series   10. Power Series 10.1 Approximating functions with polynomials 10.2 Properties of Power series 10.3 Taylor series 10.4 Working with Taylor series   11. Parametric and Polar Curves 11.1 Parametric equations 11.2 Polar coordinates 11.3 Calculus in polar coordinates 11.4 Conic sections   12. Vectors and Vector-Valued Functions 12.1 Vectors in the plane 12.2 Vectors in three dimensions 12.3 Dot products 12.4 Cross products 12.5 Lines and curves in space 12.6 Calculus of vector-valued functions 12.7 Motion in space 12.8 Length of curves 12.9 Curvature and normal vectors   13. Functions of Several Variables 13.1 Planes and surfaces 13.2 Graphs and level curves 13.3 Limits and continuity 13.4 Partial derivatives 13.5 The Chain Rule 13.6 Directional derivatives and the gradient 13.7 Tangent planes and linear approximation 13.8 Maximum/minimum problems 13.9 Lagrange multipliers   14. Multiple Integration 14.1 Double integrals over rectangular regions 14.2 Double integrals over general regions 14.3 Double integrals in polar coordinates 14.4 Triple integrals 14.5 Triple integrals in cylindrical and spherical coordinates 14.6 Integrals for mass calculations 14.7 Change of variables in multiple integrals   15. Vector Calculus 15.1 Vector fields 15.2 Line integrals 15.3 Conservative vector fields 15.4 Green’s theorem 15.5 Divergence and curl 15.6 Surface integrals 15.6 Stokes’ theorem 15.8 Divergence theorem  

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. Figures are designed to help today’s visually oriented learners. They are conceived to convey important ideas and facilitate learning, annotated to lead students through the key ideas, and rendered using the latest software for unmatched clarity and precision. Comprehensive exercise sets provide for a variety of student needs and are consistently structured and labeled to facilitate the creation of homework assignments by inspection. 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. Examples are plentiful and stepped out in detail. Within examples, each step is annotated to help students understand what took place in that step. Quick Check exercises punctuate the narrative at key points to test understanding of basic ideas and encourage students to read with pencil in hand. The MyMathLab course for the text features the following: More than 7,000 assignable exercises 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. 700 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 make the most of the Interactive Figures by including them in homework assignments. A “Getting Ready for Calculus” chapter, with built-in diagnostic tests, identifies each student’s gaps in skills and provides individual remediation directly to those skills that are lacking. Ready-to-Go Courses designed by experienced instructors miminize the start-up time for new MyMathLab users. 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. 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. This book is an expanded version of Calculus: Early Transcendentals by the same authors. It contains an entire chapter devoted to differential equations and additional sections on other topics (Newton’s method, surface area of solids of revolution, and hyperbolic functions). Most sections also contain additional exercises, many of them mid-level skills exercises.