Parametric Plots
what are parametric equations
how to plot them
common parametrizations: ellipses, lines and segments, tubes and horns
slopes of tangent lines (hence maximization/minimization)

Vectors
manipulating vectors graphically and algebraically
sums, differences, scalar multiples
lengths
dot product: definition, relationship to angle between, properties
push (projection)
position/velocity/acceleration, normal and tangential components
parametric equations of lines: parallel, perpendicular, intersections

Perpendicularity
cross product: definition, relationship to angle between, right hand rule, properties
equations (xyz and parametric) of planes in 3D
interactions between planes and lines in 3D
finding perpendicular unit vectors that span a plane (for plotting)
unit tangent, normal, binormal vectors

Gradient
definition of gradient
direction of greatest increase of a function
perpendicularity to level curves/surfaces
minimizing/maximizing a function
minimizing/maximizing subject to a constraint (Lagrange multipliers)
understanding when a function will have a minimim/maximum
local extrema; 2nd Derivative test
chain rule

Vector Fields and Their Trajectories
what is a vector field, how to visualize
what are trajectories, visually and algebraically
what are sinks and sources visually
gradient fields are special vector fields
eyeballing vector field flow across/along a curve; looking at tangential and normal components