Week 4 -- Sections 3.3-3.5

Short-term objectives

  1. Recognize discontinuities and places of nondifferentiability in functions R^n -> R^p, and evaluate routine limits of such functions. (Sec. 3.3, 3.4)
  2. Construct the differential to a function R^n -> R^p at a point, and use it to estimate the change in the function's value for a small change in its argument. (Sec. 3.4)
  3. Calculate differentials and partial derivatives of composite functions, R^n -> R^m -> R^p. (Sec. 3.5)

Long-term objectives

  1. Distinguish the various geometrical representations/interpretations of vector-valued functions of a vector argument. (Sec. 3.3)
  2. Understand the "best linear approximation" interpretation of partial derivatives. (Sec. 3.4)
  3. Understand how the chain rule follows naturally from the "best linear approximation" interpretation. (Sec. 3.5)