
 9. Vectors and the Geometry of Space
 ThreeDimensional Coordinate Systems
 Vectors
 The Dot Product
 The Cross Product
 Equations of Lines and Planes
 Functions and Surfaces
 Cylindrical and Spherical Coordinates
 10. Vector Functions
 Vector Functions and Space Curves
 Derivatives and Integrals of Vector Functions
 Arc Length and Curvature
 Motion in Space
 Parametric Surfaces
 11. Partial Derivatives
 Functions of Several Variables
 Limits and Continuity
 Partial Derivatives
 Tangent Planes and Linear Approximations
 The Chain Rule
 Directional Derivatives and the Gradient Vector
 Maximum and Minimum Values
 Lagrange Multipliers
 12. Multiple Integrals
 Double Integrals over Rectangles
 Iterated Integrals
 Double Integrals over General Regions
 Double Integrals in Polar Coordinates
 Applications of Double Integrals
 Surface Area
 Triple Integrals
 Triple Integrals in Cylindrical and Spherical Coordinates
 Change of Variables in Multiple Integrals
 13. Vector Calculus
 Vector Fields
 Line Integrals
 The Fundamental Theorem for Line Integrals
 Green's Theorem
 Curl and Divergence
 Surface Integrals
 Stokes' Theorem
 The Divergence Theorem
 Summary
