## Learning expectations for the midterm

• Be able to find parameterizations of basic curves such as line segments, and circles.
• Be able to find a parameterization of a curve given as the intersection of two surfaces.
• Be able to find the intersection (if it exists) of two parameterized curves.
• Be able to take the derivative of a vector valued function and have facility with the product rules and the chain rule. Use properties of cross and dot product to simplify expressions involving derivatives
• Be able to find the tangent lines to a curve at a point. Be able to solve more involved problems involving tangent lines (e.g. "at what point on the curve is the tangent line normal to the plane...").
• Be able to compute the arc length of a curve.
• Be able to reparemeterize a curve by arclength.
• Know the conceptual definition of curvature and be able to compute curvature from a parameterization.
• Know the conceptual definition of curvature as well as both computationally useful formulas.
• Know the definition of torsion and its meaning.
• Be able to compute the osculating plane and osculating circle to a curve.
• Know Newton's law of motion and be able to determine the motion of a particle under the influence of a force in simple cases. In particular, you should know the cases we did in class and in the book (thrown baseball, skier on a hill).
• Know the tangential and normal components of acceration.
• Be able to state Kepler's three laws.
• Know the proof of the conservation of angular momentum (done in class for planetary motion), well enough to derive conservation laws in similar circumstances.
• Be able to draw a plot of a simple vector field.
• Know the definition of conservative vector field well enough to work with it in simple cases.
• Be able to integrate a (scalar valued) function over a curve.
• Be able to integrate a vector field over a curve (a.k.a. a work integral).
• Know the fundamental theorem of line integrals.