1. Functions 1.1 Review of functions 1.2 Representing functions 1.3 Trigonometric functions 1.4 Trigonometric functions   2. Limits 2.1 The idea of limits 2.2 Definitions of limits 2.3 Techniques for computing limits 2.4 Infinite limits 2.5 Limits at infinity 2.6 Continuity 2.7 Precise definitions of limits   3. Derivatives 3.1 Introducing the derivative 3.2 Working with derivatives 3.3 Rules of differentiation 3.4 The product and quotient rules 3.5 Derivatives of trigonometric functions 3.6 Derivatives as rates of change 3.7 The Chain Rule 3.8 Implicit differentiation 3.9 Related rates   4. Applications of the Derivative 4.1 Maxima and minima 4.2 What derivatives tell us 4.3 Graphing functions 4.4 Optimization problems 4.5 Linear approximation and differentials 4.6 Mean Value Theorem 4.7 L’Hôpital’s Rule 4.8 Newton’s Method 4.9 Antiderivatives   5. Integration 5.1 Approximating areas under curves 5.2 Definite integrals 5.3 Fundamental Theorem of Calculus 5.4 Working with integrals 5.5 Substitution rule   6. Applications of Integration 6.1 Velocity and net change 6.2 Regions between curves 6.3 Volume by slicing 6.4 Volume by shells 6.5 Length of curves 6.6 Surface area 6.7 Physical applications   7. Logarithmic and Exponential Functions 7.1 Inverse functions 7.2 The natural logarithmic and exponential functions 7.3 Logarithmic and exponential functions with other bases 7.4 Exponential models 7.5 Inverse trigonometric functions 7.6 L’ Hôpital’s Rule and growth rates of functions 7.7 Hyperbolic functions   8. Integration Techniques 8.1 Basic approaches 8.2 Integration by parts 8.3 Trigonometric integrals 8.4 Trigonometric substitutions 8.5 Partial fractions 8.6 Other integration strategies 8.7 Numerical integration 8.8 Improper integrals 8.9 Introduction to differential equations   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

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, the most challenging content in Calculus 2 for students, has been spread over two chapters to help clarify and pace it more effectively. Chapter 9, 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 10, 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 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. New topics—several topics that were addressed in Guided Projects in the first edition are now, at the urging of users, included the main text. We now have complete sections with a full complement of exercises on: Newton’s method Surface area of solids of revolution Hyperbolic functions A new introductory section to the standard chapter on integration techniques. 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. 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.