10 Vectors and the Geometry of Space 10.1 Vectors in the Plane 10.2 Vectors in Space 10.3 The Dot Product 10.4 The Cross Product 10.5 Lines and Planes in Space 10.6 Surfaces in Space 11 Vector-Valued Functions 11.1 Vector-Valued Functions 11.

2 The Calculus of Vector-Valued Functions 11.3 Motion in Space 11.4 Curvature 11.5 Tangent and Normal Vectors 12 Functions of Several Variables and Differentiation 12.1 Functions of Several Variables 12.2 Limits and Continuity 12.3 Partial Derivatives 12.4 Tangent Planes and Linear Approximations 12.

5 The Chain Rule 12.6 The Gradient and Directional Derivatives 12.7 Extrema of Functions of Several Variables 12.8 Constrained Optimization and Lagrange Multipliers 13 Multiple Integrals 13.1 Double Integrals 13.2 Area, Volume and Center of Mass 13.3 Double Integrals in Polar Coordinates 13.4 Surface Area 13.

5 Triple Integrals 13.6 Cylindrical Coordinates 13.7 Spherical Coordinates 13.8 Change of Variables in Multiple Integrals 14 Vector Calculus 14.1 Vector Fields 14.2 Line Integrals 14.3 Independence of Path and Conservative Vector Fields 14.4 Green's Theorem 14.

5 Curl and Divergence 14.6 Surface Integrals 14.7 The Divergence Theorem 14.8 Stokes' Theorem.