Week 1 -- Sections 1.1-1.4

Learning Objectives (Skills)

Short term ("This will be on the test.")

  1. Find a parametric representation for a plane (defined by an equation or by geometric conditions). (Sec. 1.2)
  2. Find the tangent vector (and tangent line) to a parametrized curve at a point, and interpret it in terms of the approximate change of the vector-valued function for a small change of the parameter. (Sec. 1.4)

Long term ("Why are we studying this?")

  1. Recognize the vector operations of addition, scalar multiplication, and dot product in various contexts: (Sec. 1.1)
  2. Appreciate the difference between points and vectors, and the dependence of the vector operations in physical space upon the choice of origin. (Sec. 1.3)
  3. Distinguish the various geometrical representations/interpretations of vector-valued functions. (Sec. 1.4)