Applications of Green’s Theorem

Triple Integrals and Applications

Triple Integrals in Spherical Coordinates

Curved Surfaces in Space

Partial Derivatives—One Variable at a Time

Green’s Theorem—Boundaries and Regions

Stokes’s Theorem and Maxwell’s Equations

More Line Integrals and Work by a Force Field

Surface Integrals and Flux Integrals

Divergence Theorem—Boundaries and Solids

Parametric Surfaces in Space

Vector Fields—Velocity, Gravity, Electricity

Fundamental Theorem of Line Integrals

Surface Area of a Solid

Curl, Divergence, Line Integrals

Triple Integrals in Cylindrical Coordinates

Vectors and the Dot Product in Space

The Cross Product of Two Vectors in Space

Double Integrals and Volume

Directional Derivatives and Gradients .

Tangent Planes and Normal Vectors to a Surface

Limits, Continuity, and Partial Derivatives

Kepler’s Laws—The Calculus of Orbits

Centers of Mass for Variable Density

Iterated Integrals and Area in the Plane