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
 VectorValued Functions
 The Calculus of VectorValued 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