Chapter 11 INFINITE SERIES
11.1 Sequences
11.2 Summing an Infinite Series
11.3 Convergence of Series with Positive Terms
11.4 Absolute and Conditional Convergence
11.5 The Ratio and Root Tests
11.6 Power Series
11.7 Taylor Series
Chapter 12 PARAMETRIC EQUATIONS, POLAR COORDINATES, AND CONIC SECTIONS
12.1 Parametric Equations
12.2 Arc Length and Speed
12.3 Polar Coordinates
12.4 Area and Arc Length in Polar Coordinates
12.5 Conic Sections
Chapter 13 VECTOR GEOMETRY
13.1 Vectors in the Plane
13.2 Vectors in Three Dimensions
13.3 Dot Product and the Angle Between Two Vectors
13.4 The Cross Product
13.5 Planes in Three-Space
13.6 Survey of Quadric Surfaces
13.7 Cylindrical and Spherical Coordinates
Chapter 14 CALCULUS OF VECTOR-VALUED FUNCTIONS
14.1 Vector-Valued Functions
14.2 Calculus of Vector-Valued Functions
14.3 Arc Length and Speed
14.4 Curvature
14.5 Motion in Three-Space
14.6 Planetary Motion According to Kepler and Newton
Chapter 15 DIFFERENTIATION IN SEVERAL VARIABLES
15.1 Functions of Two or More Variables
15.2 Limits and Continuity in Several Variables
15.3 Partial Derivatives
15.4 Differentiability, Linear Approximation,and Tangent Planes
15.5 The Gradient and Directional Derivatives
15.6 The Chain Rule
15.7 Optimization in Several Variables
15.8 Lagrange Multipliers: Optimizing with a Constraint
Chapter 16 MULTIPLE INTEGRATION
16.1 Integration in Several Variables
16.2 Double Integrals over More General Regions
16.3 Triple Integrals
16.4 Integration in Polar, Cylindrical, and Spherical Coordinates
16.5 Change of Variables
Chapter 17 LINE AND SURFACE INTEGRALS
17.1 Vector Fields
17.2 Line Integrals
17.3 Conservative Vector Fields
17.4 Parametrized Surfaces and Surface Integrals
17.5 Surface Integrals of Vector Fields
Chapter 18 FUNDAMENTAL THEOREMS OF VECTOR ANALYSIS
18.1 Green’s Theorem
18.2 Stokes’ Theorem
18.3 Divergence Theorem