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Tables and Other Integration Techniques. 8.7 Indeterminate Forms and L’Hopital’s Rule.

Chapter 9: Infinite Series.

9.1 Sequences. 9.2 Series and Convergence. Section Project: Cantor’s Disappearing TTable. 9.3 The Integral Test and p-Series. Section Project: The Harmonic Series. 9.4 Comparisons of Series. Section Project: Solera Method. 9.5 Alternating Series. 9.6 The Ratio and Root Tests. 9.7 Taylor Polynomials and Approximations. 9.8 Power Series. 9.9 Representation of Functions by Power Series. 9.10 Taylor and Maclaurin Series.

Chapter 10: Conics, Parametric Equations, and Polar Coordinates.

10.1 Conics and Calculus. 10.2 Plane Curves and Parametric Equations. Section Project: Cycloids. 10.3 Parametric Equations and Calculus. 10.4 Polar Coordinates and Polar Graphs. Section Project: Anamorphic Art. 10.5 Area and Arc Length in Polar Coordinates. 10.6 Polar Equations of Conics and Kepler’s Laws.

Chapter 11: Vectors and the Geometry of Space.

11.1 Vectors in the Plane. 11.2 Space Coordinates and Vectors in Space. 11.3 The Dot Product of Two Vectors. 11.4 The Cross Product of Two Vectors in Space. 11.5 Lines and Planes in Space. Section Project: Distances in Space. 11.6 Surfaces in Space. 11.7 Cylindrical and Spherical Coordinates.

Chapter 12: Vector-Valued Functions.

12.1 Vector-Valued Functions. Section Project: Witch of Agnesi. 12.2 Differentiation and Integration of Vector-Valued Functions. 12.3 Velocity and Acceleration. 12.4 Tangent Vectors and Normal Vectors. 12.5 Arc Length and Curvature.

Chapter 13: Functions of Several VariTables.

13.1 Introduction to Functions of Several VariTables. 13.2 Limits and Continuity. 13.3 Partial Derivatives. Section Project: MoirÃ© Fringes. 13.4 Differentials. 13.5 Chain Rules for Functions of Several VariTables. 13.6 Directional Derivatives and Gradients. 13.7 Tangent Planes and Normal Lines. Section Project: Wildflowers. 13.8 Extrema of Functions of Two VariTables. 13.9 Applications of Extrema of Functions of Two VariTables. Section Project: Building a Pipeline. 13.10 Lagrange Multipliers.

Chapter 14: Multiple Integration.

14.1 Iterated Integrals and Area in the Plane. 14.2 Double Integrals and Volume. 14.3 Change of VariTables: Polar Coordinates. 14.4 Center of Mass and Moments of Inertia. Section Project: Center of Pressure on a Sail. 14.5 Surface Area. Section Project: Capillary Action. 14.6 Triple Integrals and Applications. 14.7 Triple Integrals in Cylindrical and Spherical Coordinates. Section Project: Wrinkled and Bumpy Spheres. 14.8 Change of VariTables: Jacobians.

Chapter 15: Vector Analysis.

15.1 Vector Fields. 15.2 Line Integrals. 15.3 Conservative Vector Fields and Independence of Path. 15.4 Green’s Theorem. Section Project: Hyperbolic and Trigonometric Functions. 15.5 Parametric Surfaces. 15.6 Surface Integrals. Section Project: Hyperboloid of One Sheet. 15.7 Divergence Theorem. 15.8 Stokes’s Theorem. Section Project: The Planimeter.

Bonus Online Material.

Chapter 16: Additional Topics in Differential Equations (please visit URL to come).

16.1 Exact First-Order Equations. 16.2 Second-Order Homogeneous Linear Equations. 16.3 Second-Order Nonhomogeneous Linear Equations. Section Project: Parachute Jump. 16.4 Series Solutions of Differential Equations.

Book Appendices.

A. Proofs of Selected Theorems. B. Integration TTables.

Online Appendices.

C. Precalculus Review (please visit URL to come). C.1 Real Numbers and the Real Number Line. C.2 The Cartesian Plane. C.3 Review of Trigonometric Functions. D. Rotation and the General Second-Degree Equation (please visit URL to come). E. Complex Numbers (please visit URL to come). F Business and Economic Applications (please visit URL to come).