CHAPTER 11 THREE-DIMENSIONAL ANALYTIC GEOMETRY AND VECTORS
11.1 Three-Dimensional Coordinate Systems
11.2 Vectors
11.3 The Dot Product
11.4 The Cross Product
11.5 Equations of Lines and Planes
11.6 Quadric Surfaces
11.7 Vector Functions and Space Curves
11.8 Arc Length and Curvature
11.9 Motion in Space: Velocity and Acceleration
11.10 Cylindrical and Spherical Coordinates

CHAPTER 12 PARTIAL DERIVATIVES
12.1 Functions of Several Variables
12.2 Limits and Continuity
12.3 Partial Derivatives
12.4 Tangent Planes and Differentials
12.5 The Chain Rule
12.6 Directional Derivatives and the Gradient Vector
12.7 Maximum and Minimum Values
12.8 Lagrange Multipliers

CHAPTER 13 MULTIPLE INTEGRALS
13.1 Double Integrals over Rectangles
13.2 Iterated Integrals
13.3 Double Integrals over General Regions
13.4 Double Integrals in Polar Coordinates
13.5 Applications of Double Integrals
13.6 Surface Area
13.7 Triple Integrals
13.8 Triple Integrals in Cylindrical and Spherical Coordinates
13.9 Change of Variables in Multiple Integrals

CHAPTER 14 VECTOR FIELDS
14.1 Vector Fields
14.2 Line Integrals
14.3 The Fundamental Theorem of Line Integrals
14.4 Green's Theorem
14.5 Curl and Divergence
14.6 Parametric Surfaces and their Area (OPTIONAL)
14.7 Surface Integrals
14.8 Stokes' Theorem
14.9 The Divergence Theorem
14.10 Summary