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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 functions1.3 Inverse, exponential, and logarithmic functions1.4 Trigonometric functions and their inverses 2. Limits2.1 The idea of limits2.2 Definitions of limits2.3 Techniques for computing limits 2.4 Infinite limits 2.5 Limits at infinity 2.6 Continuity2.7 Precise definitions of limits 3. Derivatives3.1 Introducing the derivative3.2 Working with derivatives3.3 Rules of differentiation3.4 The product and quotient rules3.5 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 functions3.10 Derivatives of inverse trigonometric functions3.11 Related rates 4. Applications of the Derivative4.1 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 Theorem4.7 L'Hopital's Rule 4.8 Newton's Method 4.9 Antiderivatives 5. Integration5.1 Approximating areas under curves5.2 Definite integrals 5.3 Fundamental Theorem of Calculus 5.4 Working with integrals 5.5 Substitution rule 6. Applications of Integration6.1 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 applications6.8 Logarithmic and exponential functions revisited6.9 Exponential models6.10 Hyperbolic functions 7. Integration Techniques7.1 Basic approaches7.2 Integration by parts 7.3 Trigonometric integrals 7.4 Trigonometric substitutions7.5 Partial fractions 7.6 Other integration strategies7.7 Numerical integration7.8 Improper integrals7.9 Introduction to differential equations 8. Sequences and Infinite Series8.1 An overview 8.2 Sequences8.3 Infinite series 8.4 The Divergence and Integral Tests8.5 The Ratio, Root, and Comparison Tests8.6 Alternating series 9. Power Series9.1 Approximating functions with polynomials9.2 Properties of Power series9.3 Taylor series9.4 Working with Taylor series 10. Parametric and Polar Curves 10.1 Parametric equations10.2 Polar coordinates 10.3 Calculus in polar coordinates 10.4 Conic sections 11. Vectors and Vector-Valued Functions11.1 Vectors in the plane11.2 Vectors in three dimensions11.3 Dot products11.4 Cross products11.5 Lines and curves in space 11.6 Calculus of vector-valued functions 11.7 Motion in space11.8 Length of curves11.9 Curvature and normal vectors 12. Functions of Several Variables12.1 Planes and surfaces12.2 Graphs and level curves12.3 Limits and continuity12.4 Partial derivatives12.5 The Chain Rule 12.6 Directional derivatives and the gradient12.7 Tangent planes and linear approximation12.8 Maximum/minimum problems12.9 Lagrange multipliers 13. Multiple Integration13.1 Double integrals over rectangular regions13.2 Double integrals over general regions13.3 Double integrals in polar coordinates13.4 Triple integrals13.5 Triple integrals in cylindrical and spherical coordinates13.6 Integrals for mass calculations13.7 Change of variables in multiple integrals 14. Vector Calculus14.1 Vector fields14.2 Line integrals14.3 Conservative vector fields14.4 Green's theorem14.5 Divergence and curl14.6 Surface integrals14.6 Stokes' theorem14.8 Divergence theorem Appendix A. Algebra ReviewAppendix B. Proofs of Selected Theorems D1. Differential Equations (online)D1.1 Basic IdeasD1.2 Direction Fields and Euler's MethodD1.3 Separable Differential EquationsD1.4 Special First-Order Differential EquationsD1.5 Modeling with Differential Equations D2. Second-Order Differential Equations (online)D2.1 Basic IdeasD2.2 Linear Homogeneous EquationsD2.3 Linear Nonhomogeneous EquationsD2.4 ApplicationsD2.5 Complex Forcing Functions
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