Calculus Early Transcendentals

For a three-semester or four-quarter calculus course covering single variable and multivariable calculus for mathematics, engineering, and science majors. This much anticipated second edition of the most successful new calculus text published in the last two decades retains the best of the first edition while introducing important advances and refinements. Authors Briggs, Cochran, and Gillett build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor, examples that are stepped out and thoughtfully annotated, and figures that are designed to teach rather than simply supplement the narrative. The authors appeal to students' geometric intuition to introduce fundamental concepts, laying a foundation for the development that follows. The groundbreaking eBook contains over 650 Interactive Figures that can be manipulated to shed light on key concepts. This text offers a superior teaching and learning experience. Here's how: *A robust MyMathLab(R) 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. *Reflects how students use a textbook-they start with the exercises and flip back for help if they need it. *Organization and presentation of content facilitates learning of key concepts, skills, and applications.1. Functions 1.1 Review of functions 1.2 Representing functions 1.3 Inverse, exponential, and logarithmic functions 1.4 Trigonometric functions and their inverses 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 Derivatives of logarithmic and exponential functions 3.10 Derivatives of inverse trigonometric functions 3.11 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'Hopital'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 6.8 Logarithmic and exponential functions revisited 6.9 Exponential models 6.10 Hyperbolic functions 7. Integration Techniques 7.1 Basic approaches 7.2 Integration by parts 7.3 Trigonometric integrals 7.4 Trigonometric substitutions 7.5 Partial fractions 7.6 Other integration strategies 7.7 Numerical integration 7.8 Improper integrals 7.9 Introduction to differential equations 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 Appendix A. Algebra Review Appendix B. Proofs of Selected Theorems D1. Differential Equations (online) D1.1 Basic Ideas D1.2 Direction Fields and Euler's Method D1.3 Separable Differential Equations D1.4 Special First-Order Differential Equations D1.5 Modeling with Differential Equations D2. Second-Order Differential Equations (online) D2.1 Basic Ideas D2.2 Linear Homogeneous Equations D2.3 Linear Nonhomogeneous Equations D2.4 Applications D2.5 Complex Forcing Functions