Calculus / William L. Briggs, Lyle Cochran ; with contributions by Bernard Gillett.

1. Functions 1.1 Review of Functions 1.2 Representing Functions 1.3 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 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 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 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 Physical Applications 7. Logarithmic and Exponential Functions 7.1 Inverse Functions 7.2 The Natural Logarithmic and Exponential Functions 7.3 Logarithmic and Exponential Functions with Other Bases 7.4 Exponential Models 7.5 Inverse Trigonometric Functions 7.6 L'Hopital's Rule Revisited and Growth Rates of Functions 8. Integration Techniques 8.1 Integration by Parts 8.2 Trigonometric Integrals 8.3 Trigonometric Substitutions 8.4 Partial Fractions 8.5 Other Integration Strategies 8.6 Numerical Integration 8.7 Improper Integrals 8.8 Introduction to Differential Equations 9. Sequences and Infinite Series 9.1 An Overview 9.2 Sequences 9.3 Infinite Series 9.4 The Divergence and Integral Tests 9.5 The Ratio, Root, and Comparison Tests 9.6 Alternating Series Review 10. Power Series 10.1 Approximating Functions with Polynomials 10.2 Power Series 10.3 Taylor Series 10.4 Working with Taylor Series 11. Parametric and Polar Curves 11.1 Parametric Equations 11.2 Polar Coordinates 11.3 Calculus in Polar Coordinates 11.4 Conic Sections 12. Vectors and Vector-Valued Functions 12.1 Vectors in the Plane 12.2 Vectors in Three Dimensions 12.3 Dot Products 12.4 Cross Products 12.5 Lines and Curves in Space 12.6 Calculus of Vector-Valued Functions 12.7 Motion in Space 12.8 Length of Curves 12.9 Curvature and Normal Vectors 13. Functions of Several Variables 13.1 Planes and Surfaces 13.2 Graphs and Level Curves 13.3 Limits and Continuity 13.4 Partial Derivatives 13.5 The Chain Rule 13.6 Directional Derivatives and the Gradient 13.7 Tangent Planes and Linear Approximation 13.8 Maximum/Minimum Problems 13.9 Lagrange Multipliers 14. Multiple Integration 14.1 Double Integrals over Rectangular Regions 14.2 Double Integrals over General Regions 14.3 Double Integrals in Polar Coordinates 14.4 Triple Integrals 14.5 Triple Integrals in Cylindrical and Spherical Coordinates 14.6 Integrals for Mass Calculations 14.7 Change of Variables in Multiple Integrals 15. Vector Calculus 15.1 Vector Fields 15.2 Line Integrals 15.3 Conservative Vector Fields 15.4 Green's Theorem 15.5 Divergence and Curl 15.6 Surface Integrals 15.6 Stokes' Theorem 15.8 Divergence Theorem

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.

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