Chapter 11: Functions of Many Variables

11.1. Functions of Two Variables
11.2. A Tour of Three-Dimensional Space
11.3. Graphs of Functions of Two Variables
11.4. Contour Diagrams
11.5. Linear Functions

Chapter 12: A Fundumental Tool: Vectors

12.1. Displacement Vectors
12.2. Vectors in General
12.3. The Dot Product
12.4. The Cross Product

Chapter 13: Differentiating Functions of Many Variables

13.1. The Partial Derivative
13.2. Computing Partial Derivatives Algebraically
13.3. Local Linearity and the Differential
13.4. Directional Derivatives
13.5. The Gradient
13.6. The Chain Rule
13.7. Second -Order Partial Derivatives
13.9. Notes on Quadratic Approximations

Chapter 14: Optimization

14.1. Local and Global Extrema
14.2. Unconstrained Optimization
14.3. Constrained Optimization

Chapter 15: Integrating Functions of Many Variables

15.1. The Definite Integral of a Function of Two Variables
15.2. Iterated Integrals
15.3. Three-Variable Integrals
15.5. Two-Variable Integrals in Polar Coordinates
15.6. Integrals in Cylindrical and Spherical Coordinates
15.8. Change of Variables in a Multiple Integral

Chapter 16: Parametric Curves

16.1. Motion in Space
16.2. Parametrized Curves
16.3. Velocity and Acceleration  Vectors

Chapter 17: Vector Fields

17.1. Vector Fields
17.2. The Flow of a Vector Field

Chapter 18: Line Integrals

18.1. The Idea of a Line Integral
18.2. Computing Line Integrals Over Parametrized Curves
18.3. Gradient Fields and Conservative Fields
18.4. Nonconservative Fields and Green's Theorem