MAT-397 lecture notes

Three-dimensional coordinate systems 

Vectors

Dot product

Cross product

Equations of lines and planes

Vector functions and space curves

Velocity and acceleration in 3-D space

Limits and continuity

Partial derivatives

Tangent planes and linear approximations

Chain rule

Directional derivative

Local and absolute extrema

Lagrange multipliers

Double integrals over rectangles

Double integrals in rectangular coordinates

Center of mass

Change of variables for double integrals

Fundamental theorem of line integrals

Green's theorem

Curl and Divergence

Parametric surfaces and surface area

Surface integrals

Stokes' theorem

Divergence theorem