1. Functions 1.1 Review of functions 1.2 Representing functions 1.3 Trigonometric functions and their inverses Review   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 Review   3. Derivatives 3.1 Introducing the derivative 3.2 Rules of differentiation 3.3 The product and quotient rules 3.4 Derivatives of trigonometric functions 3.5 Derivatives as rates of change 3.6 The Chain Rule 3.7 Implicit differentiation 3.8 Derivatives of inverse trigonometric functions 3.9 Related rates Review   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 Review   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 Review   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 6.8 Hyperbolic functions Review   7. Logarithmic and Exponential Functions 7.1 Inverse functions 7.2 The natural logarithm and exponential functions 7.3 Logarithmic and exponential functions with general bases 7.4 Exponential models 7.5 Inverse trigonometric functions 7.6 L'Hôpital's rule and growth rates of functions Review   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 Review   9. Differential Equations 9.1 Basic ideas 9.2 Direction fields and Euler's method 9.3 Separable differential equations 9.4 Special first-order differential equations 9.5 Modeling with differential equations Review   10. Sequences and Infinite Series 10.1 An overview 10.2 Sequences 10.3 Infinite series 10.4 The Divergence and Integral Tests 10.5 The Ratio, Root, and Comparison Tests 10.6 Alternating series Review   11. Power Series 11.1 Approximating functions with polynomials 11.2 Properties of power series 11.3 Taylor series 11.4 Working with Taylor series Review   12. Parametric and Polar Curves 12.1 Parametric equations 12.2 Polar coordinates 12.3 Calculus in polar coordinates 12.4 Conic sections Review   13. Vectors and Vector-Valued Functions 13.1 Vectors in the plane 13.2 Vectors in three dimensions 13.3 Dot products 13.4 Cross products 13.5 Lines and curves in space 13.6 Calculus of vector-valued functions 13.7 Motion in space 13.8 Length of curves 13.9 Curvature and normal vectors Review   14. Functions of Several Variables 14.1 Planes and surfaces 14.2 Graphs and level curves 14.3 Limits and continuity 14.4 Partial derivatives 14.5 The Chain Rule 14.6 Directional derivatives and the gradient 14.7 Tangent planes and linear approximation 14.8 Maximum/minimum problems 14.9 Lagrange multipliers Review   15. Multiple Integration 15.1 Double integrals over rectangular regions 15.2 Double integrals over general regions 15.3 Double integrals in polar coordinates 15.4 Triple integrals 15.5 Triple integrals in cylindrical and spherical coordinates 15.6 Integrals for mass calculations 15.7 Change of variables in multiple integrals Review   16. Vector Calculus 16.1 Vector fields 16.2 Line integrals 16.3 Conservative vector fields 16.4 Green's theorem 16.5. Divergence and curl 16.6 Surface integrals 16.6 Stokes' theorem 16.8 Divergence theorem Review

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 to minimize 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 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.