Calculus: Early Transcendentals, Global Edition

About our authors William Briggs has been on the mathematics faculty at the University of Colorado at Denver for 23 years. He received his BA in mathematics from the University of Colorado and his MS and PhD in applied mathematics from Harvard University. He teaches undergraduate and graduate courses throughout the mathematics curriculum, with a special interest in mathematical modeling and differential equations as it applies to problems in the biosciences. He has written a quantitative reasoning textbook, Using and Understanding Mathematics; an undergraduate problem solving book, Ants, Bikes, and Clocks; and two tutorial monographs, The Multigrid Tutorial and The DFT: An Owner's Manual for the Discrete Fourier Transform. He is the Society for Industrial and Applied Mathematics (SIAM) Vice President for Education, a University of Colorado President's Teaching Scholar, a recipient of the Outstanding Teacher Award of the Rocky Mountain Section of the Mathematical Association of America (MAA), and the recipient of a Fulbright Fellowship to Ireland.Lyle Cochran is a professor of mathematics at Whitworth University in Spokane, Washington. He holds BS degrees in mathematics and mathematics education from Oregon State University and a MS and PhD in mathematics from Washington State University. He has taught a wide variety of undergraduate mathematics courses at Washington State University, Fresno Pacific University, and since 1995 at Whitworth University. His expertise is in mathematical analysis, and he has a special interest in the integration of technology and mathematics education. He has written technology materials for leading calculus and linear algebra textbooks including the Instructor's Mathematica Manual for Linear Algebra and Its Applications by David C. Lay and the Mathematica Technology Resource Manual for Thomas' Calculus. He is a member of the MAA and a former chair of the Department of Mathematics and Computer Science at Whitworth University.Bernard Gillett is a Senior Instructor at the University of Colorado at Boulder; his primary focus is undergraduate education. He has taught a wide variety of mathematics courses over a 20-year career, receiving 5 teaching awards in that time. Bernard authored a software package for algebra, trigonometry, and precalculus; the Student's Guide and Solutions Manual and the Instructor's Guide and Solutions Manual for Using and Understanding Mathematics by Briggs and Bennett; and the Instructor's Resource Guide and Test Bank for Calculus and Calculus: Early Transcendentals by Briggs, Cochran and Gillett. Bernard is also an avid rock climber and has published 4 climbing guides for the mountains in and surrounding Rocky Mountain National Park.Eric Schulz has been teaching mathematics at Walla Walla Community College since 1989 and began his work with Mathematica in 1992. He has an undergraduate degree in mathematics from Seattle Pacific University and a graduate degree in mathematics from the University of Washington. Eric loves working with students and is passionate about their success. His interest in innovative and effective uses of technology in teaching mathematics has remained strong throughout his career. He is the developer of the Basic Math Assistant, Classroom Assistant, and Writing Assistant palettes that ship in Mathematica worldwide. He is an author on multiple textbooks: Calculus and Calculus: Early Transcendentals with Briggs, Cochran and Gillett, and Precalculus with Sachs and Briggs, where he writes, codes and creates dynamic eTexts combining narrative, videos and Interactive Figures using Mathematica and CDF technology.

• 1. Functions 1.1 Review of Functions1.2 Representing Functions1.3 Inverse, Exponential, and Logarithmic Functions1.4 Trigonometric Functions and Their InversesReview Exercises2. Limits 2.1 The Idea of Limits2.2 Definitions of Limits2.3 Techniques for Computing Limits2.4 Infinite Limits2.5 Limits at Infinity2.6 Continuity2.7 Precise Definitions of LimitsReview Exercises3. Derivatives 3.1 Introducing the Derivative3.2 The Derivative as a Function3.3 Rules of Differentiation3.4 The Product and Quotient Rules3.5 Derivatives of Trigonometric Functions3.6 Derivatives as Rates of Change3.7 The Chain Rule3.8 Implicit Differentiation3.9 Derivatives of Logarithmic and Exponential Functions3.10 Derivatives of Inverse Trigonometric Functions3.11 Related RatesReview Exercises4. Applications of the Derivative 4.1 Maxima and Minima4.2 Mean Value Theorem4.3 What Derivatives Tell Us4.4 Graphing Functions4.5 Optimization Problems4.6 Linear Approximation and Differentials4.7 L'Hôpital's Rule4.8 Newton's Method4.9 AntiderivativesReview Exercises5. Integration 5.1 Approximating Areas under Curves5.2 Definite Integrals5.3 Fundamental Theorem of Calculus5.4 Working with Integrals5.5 Substitution RuleReview Exercises6. Applications of Integration 6.1 Velocity and Net Change6.2 Regions Between Curves6.3 Volume by Slicing6.4 Volume by Shells6.5 Length of Curves6.6 Surface Area6.7 Physical ApplicationsReview Exercises7. Logarithmic, Exponential, and Hyperbolic Functions 7.1 Logarithmic and Exponential Functions Revisited7.2 Exponential Models7.3 Hyperbolic FunctionsReview Exercises8. Integration Techniques 8.1 Basic Approaches8.2 Integration by Parts8.3 Trigonometric Integrals8.4 Trigonometric Substitutions8.5 Partial Fractions8.6 Integration Strategies8.7 Other Methods of Integration8.8 Numerical Integration8.9 Improper IntegralsReview Exercises9. Differential Equations 9.1 Basic Ideas9.2 Direction Fields and Euler's Method9.3 Separable Differential Equations9.4 Special First-Order Linear Differential Equations9.5 Modeling with Differential EquationsReview Exercises10. Sequences and Infinite Series 10.1 An Overview10.2 Sequences10.3 Infinite Series10.4 The Divergence and Integral Tests10.5 Comparison Tests10.6 Alternating Series10.7 The Ratio and Root Tests10.8 Choosing a Convergence TestReview Exercises11. Power Series 11.1 Approximating Functions with Polynomials11.2 Properties of Power Series11.3 Taylor Series11.4 Working with Taylor SeriesReview Exercises12. Parametric and Polar Curves 12.1 Parametric Equations12.2 Polar Coordinates12.3 Calculus in Polar Coordinates12.4 Conic SectionsReview Exercises13. Vectors and the Geometry of Space 13.1 Vectors in the Plane13.2 Vectors in Three Dimensions13.3 Dot Products13.4 Cross Products13.5 Lines and Planes in Space13.6 Cylinders and Quadric SurfacesReview Exercises14. Vector-Valued Functions 14.1 Vector-Valued Functions14.2 Calculus of Vector-Valued Functions14.3 Motion in Space14.4 Length of Curves14.5 Curvature and Normal VectorsReview Exercises15. Functions of Several Variables 15.1 Graphs and Level Curves15.2 Limits and Continuity15.3 Partial Derivatives15.4 The Chain Rule15.5 Directional Derivatives and the Gradient15.6 Tangent Planes and Linear Approximation15.7 Maximum/Minimum Problems15.8 Lagrange MultipliersReview Exercises16. Multiple Integration 16.1 Double Integrals over Rectangular Regions16.2 Double Integrals over General Regions16.3 Double Integrals in Polar Coordinates16.4 Triple Integrals16.5 Triple Integrals in Cylindrical and Spherical Coordinates16.6 Integrals for Mass Calculations16.7 Change of Variables in Multiple IntegralsReview Exercises17. Vector Calculus 17.1 Vector Fields17.2 Line Integrals17.3 Conservative Vector Fields17.4 Green's Theorem17.5 Divergence and Curl17.6 Surface Integrals17.7 Stokes' Theorem17.8 Divergence TheoremReview ExercisesD2 Second-Order Differential Equations ONLINE D2.1 Basic IdeasD2.2 Linear Homogeneous EquationsD2.3 Linear Nonhomogeneous EquationsD2.4 ApplicationsD2.5 Complex Forcing FunctionsReview ExercisesAppendices Proofs of Selected TheoremsAlgebra Review ONLINEComplex Numbers ONLINEAnswers Index Table of Integrals