MTH 2321 - Calculus III

Vectors & the Geometry of Space
Vectors in Planes
Vectors in Space
The Dot Product: Components & Projections
The Cross Product
Lines & Planes in Space
Surfaces in Space

Vector-Valued Functions
The Calculus of Vector-Valued Functions
Motion in Space
Curvature
Tangent Normal Vectors

Functions of Several Variables & Partial Differentiation
Functions of Several Variables
Limits and Continuity
Partial Derivatives
Tangent Planes & Linear Approximations
The Chain Rule
The Gradient and Directional Derivatives
Extrema of Functions of Several Variables
Constrained Optimization and Lagrange Multipliers

Multiple Integrals
Double Integrals
Area, Volume and Center of Mass
Double Integrals in Polar Coordinates
Surface Area
Triple Integrals: Mass and Center of Mass
Cylindrical Coordinates
Spherical Coordinates
Change of Variables in Multiple Integrals

Vector Calculus
Vector Fields
Line Integrals
Independence of Path & Conservative Vector Fields
Green's Theorem
Curl and Divergence
Surface Integrals: Parametric Representation of Surfaces
The Divergence Theorem
Stokes' Theorem