8. Integration  Techniques, L'Hôspital's Rule, and Improper Integration

    8.8 Improper Integrals

9. Infinite Series

   9.1 Sequences
   9.2 Series and Convergence
   9.3 The Integral Test and P- Series
   9.4 Comparisons of Series
   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

10. Conics, Parametric Equations, and Polar Coordinates

10.2 Plane Curves and Parametric Equations
10.3 Parametric Equations and Calculus
10.4 Polar Coordinates and Polar Graphs
10.5 Area and Arc Length in Polar Coordinates

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 TwoVectors
11.4 The Cross Product of TwoVectors in Space
11.5 Lines and Planes in Space
11.6 Surfaces in Space
11.7 Cylindrical and Spherical Coordinates
 

12. Vector-Valued Functions

12.1 Vector Valued Functions
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

13. Functions of Several Variables
13.1 Introduction to Functions of Several Variables.
13.2 Limits and Continuity
13.3 Partial Derivative
13.4 Differentials
13.5 Chain Rules for Functions of Several Variables
13.6 Directional Derivatives andGradients
13.7 Tangent Planes and Normal Lines
13.8 Extrema of Functions of Two Variables
13.9 Applications of Extrema of Functions of Two Variables
13.10 Lagrange Multipliers

14. Multiple Integration
14.1 Iterated Integrals and Area in the Plane
14.2 Double Integrals and Volume
14.3 Change of Variables: Polar Coordinates
14.6 Triple Integrals and Applications

Appendix B Proofs of Selected Theorems
Appendix C  Integration Tables