## Learning expectations for Midterm 1

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.