9.1 Three-Dimensional Coordinate Systems
9.2 Vectors
9.3 The Dot Product
9.4 The Cross Product
9.5 Equations of Lines and Planes
9.6 Functions and Surfaces
9.7 Cylindrical and Spherical Coordinates
Chapter 9. Vectors
and the Geometry of Space
9.1 Three-Dimensional Coordinate Systems
9.2 Vectors
9.3 The Dot Product
9.4 The Cross Product
9.5 Equations of Lines and Planes
9.6 Functions and Surfaces
9.7 Cylindrical and Spherical Coordinates
Chapter 10. Vector Functions
10.1 Vector Functions and Space Curves
10.2 Derivatives and Integrals of Vector Functions
10.3 Arc Length and Curvature
10.4 Motion in Space
10.5 Parametric Surfaces
Chapter 11. Partial Derivatives
11.1 Functions of Several Variables
11.2 Limits and Continuity
11.3 Partial Derivatives
11.4 Tangent Planes and Linear Approximations
11.5 The Chain Rule
11.6 Directional Derivatives and the Gradient Vector
11.7 Maximum and Minimum Values
11.8 Lagrange Multipliers
Chapter 12. Multiple Integrals
12.1 Double Integrals over Rectangles
12.2 Iterated Integrals
12.3 Double Integrals over General Regions
12.4 Double Integrals in Polar Coordinates
12.6 Surface Area
12.7 Triple Integrals
12.8 Triple Integrals in Cylindrical and Spherical Coordinates
12.9 Change of Variables in Multiple Integrals
Chapter 13. Vector Calculus
13.1 Vector Fields
13.2 Line Integrals
13.3 The Fundamental Theorem for Line Integrals
13.4 Green's Theorem