Multivariable Calculus
Chapter 12
12.1 Three-Dimensional Coordinate Systems
12.2 Vectors
12.3 The Dot Product
12.4 The Cross Product
12.5 Equations of Lines and Planes
Chapter 13
13.1 Vector Functions and Space Curves
13.2 Derivatives and Integrals of Vector Functions
Chapter 14
14.1 Functions of Several Variables
14.2 Limits and Continuity
14.3 Partial Derivatives
14.4 Tangent Planes and Linear Approximations
14.5 The Chain Rule
14.6 Directional Derivatives and the Gradient
14.7 Maximum and Minimum Values
14.8 Lagrange Multipliers
Chapter 15
15.1 Double Integrals
15.2 Double Integrals Over General Regions
15.4 Applications of Double Integrals
15.6 Triple Integrals
15.9 Change of Variables
15.3 Polar Coordinates
15.7 Cylindrical Coordinates
15.8 Spherical Coordinates
Chapter 16
16.2 Line Integrals
16.1 Vector Fields
16.3 The Fundamental Theorem for Line Integrals
16.4 Green's Theorem
16.5 Curl and Divergence
16.6 Parametric Surfaces
16.7 Surface Integrals
16.8 Stokes' Theorem
16.9 The Divergence Theorem
16.10 Summary of Integration Theorems