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ALERTcourse syllabus to ensure that you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, including customized versions for individual schools, and registrations are not transferable. In addition, you may need a CourseID, provided by your instructor, to register for and use Pearson's MyLab & Mastering products. Packages Access codes for Pearson's MyLab & Mastering products may not be included when purchasing or renting from companies other than Pearson; check with the seller before completing your purchase. Used or rental books If you rent or purchase a used book with an access code, the access code may have been redeemed previously and you may have to purchase a new access code. Access codes Access codes that are purchased from sellers other than Pearson carry a higher risk of being either the wrong ISBN or a previously redeemed code. Check with the seller prior to purchase. --Drawing on their decades of teaching experience, William Briggs and Lyle Cochran have created a calculus text that carries the teacher's voice beyond the classroom. That voice-evident in the narrative, the figures, and the questions interspersed in the narrative-is a master teacher leading readers to deeper levels of understanding. The authors appeal to readers' geometric intuition to introduce fundamental concepts and lay the foundation for the more rigorous development that follows. Comprehensive exercise sets have received praise for their creativity, quality, and scope. This book is an expanded version of Calculus: Early Transcendentals by the same authors, with an entire chapter devoted to differential equations, additional sections on other topics, and additional exercises in most sections.
Contents
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 Rules of differentiation3.3 The product and quotient rules3.4 Derivatives of trigonometric functions 3.5 Derivatives as rates of change 3.6 The Chain Rule 3.7 Implicit differentiation 3.8 Derivatives of logarithmic and exponential functions3.9 Derivatives of inverse trigonometric functions3.10 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 Integration Strategies7.2 Integration by parts 7.3 Trigonometric integrals 7.4 Trigonometric substitutions7.5 Partial fractions 7.6 Other integration strategies7.7 Numerical integration7.8 Improper integrals 8. Differential Equations 8.1 Basic ideas 8.2 Direction fields and Euler's method8.3 Separable differential equations 8.4 Special first-order differential equations8.5 Modeling with differential equations 9. Sequences and Infinite Series9.1 An overview 9.2 Sequences9.3 Infinite series 9.4 The Divergence and Integral Tests9.5 The Ratio, Root, and Comparison Tests9.6 Alternating series 10. Power Series10.1 Approximating functions with polynomials10.2 Properties of Power series10.3 Taylor series10.4 Working with Taylor series 11. Parametric and Polar Curves 11.1 Parametric equations11.2 Polar coordinates 11.3 Calculus in polar coordinates 11.4 Conic sections 12. Vectors and Vector-Valued Functions12.1 Vectors in the plane12.2 Vectors in three dimensions12.3 Dot products12.4 Cross products12.5 Lines and curves in space 12.6 Calculus of vector-valued functions 12.7 Motion in space12.8 Length of curves12.9 Curvature and normal vectors 13. Functions of Several Variables13.1 Planes and surfaces13.2 Graphs and level curves13.3 Limits and continuity13.4 Partial derivatives13.5 The Chain Rule 13.6 Directional derivatives and the gradient13.7 Tangent planes and linear approximation13.8 Maximum/minimum problems13.9 Lagrange multipliers 14. Multiple Integration14.1 Double integrals over rectangular regions14.2 Double integrals over general regions14.3 Double integrals in polar coordinates14.4 Triple integrals14.5 Triple integrals in cylindrical and spherical coordinates14.6 Integrals for mass calculations14.7 Change of variables in multiple integrals 15. Vector Calculus15.1 Vector fields15.2 Line integrals15.3 Conservative vector fields15.4 Green's theorem15.5 Divergence and curl15.6 Surface integrals15.6 Stokes' theorem15.8 Divergence theorem Appendix A. Algebra ReviewAppendix B. Proofs of Selected Theorems
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