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