3-Dimensional Coordinate System
Vectors, Lines, Surfaces, & Solids
The Dot Product
The Cross Product
Planes
Quadric Surfaces
Vector Functions
Arc Length
Properties of curves in 3D Space
Functions of Several Variables
Limits of Multivariable Functions
Derivatives of Multivariable Functions
Tangent Planes & Applications
Directional Derivatives
The Chain Rule
Minimum and Maximum Values
Lagrange Multipliers
Double integrals on rectangular regions
Double Integrals Over General Regions
Triple Integrals in Rectangular Coordinates
Double Integrals in Polar Coordinates
Triple Integrals in Cylindrical Coordinates
Triple Integrals in Spherical Coordinates
Coordinate Transformation & Integration
Vector Fields
Line Integrals
The Fundamental Theorem of Conservative Vector Fields
Scalar Surface Integrals
Vector Surface Integrals
Green’s Theorem
Stokes’ Theorem
The Divergence Theorem