You should be able to:
Match plots of curves with vector valued functions.
Find parameterizations of curves which have been given geometrically (e.g. lines, circles, intersections of two surfaces).
Find derivatives of expressions involving vector valued functions, dot products, and cross products. Simplify such expressions using geometric properties of cross product and dot product.
Find the arclength of a curve.
Reparameterize a curve by arclength.
Know three formulas for the curvature of a curve and be able to apply them to compute curvature and/or answer conceptual questions.
Compute the unit tangent vector, normal vector, and binormal vector to a curve at a point.
Find the osculating plane and circle to a curve at a point.
Find position the position vector of a curve when given the acceleration vector; apply Newton's law of motion.
Find the tangential and normal components of acceleration. Understand the intuitive meaning of each.
Know the definition of a conservative vector field and a potential
function.