3-Dimensional Coordinate System
Vectors
The Dot Product
The Cross Product
Equations of Lines and Planes
Cylinders and Quadric Surfaces
Vector-Valued Functions
Arc Length and Curvature
Motion in Space
Functions of Several Variables
Limits and Continuity
Partial Derivatives
Tangent Planes and Linear Approximations
The Chain Rule
Directional Derivatives and Gradients
Gradients and Tangent Planes
Maximum and Minimum Values
Lagrange Multipliers
Double Integrals over Rectangles
Double Integrals over General Regions
Change of Coordinates
Change of Variables in Multiple Integrals
Double Integrals in Polar Coordinates
Triple Integrals in Rectangular Coordinates
Triple Integrals in Cylindrical Coordinates
Triple Integrals in Spherical Coordinates
Vector Fields
Line Integrals
The Fundamental Theorem for Line Integrals
Green’s Theorem
Parametric Surfaces
Surface Integrals
Stokes’ Theorem
The Divergence Theorem