Derivatives of multivariable functions

Learning objectives

  • Interpret and use partial derivatives as multipliers with units
  • Use the master equation \Delta z \approx (\partial z/\partial x) \Delta x + (\partial z/\partial y) \Delta y for z = f(x, y) and small \Delta x and \Delta y
  • Make numerical approximations of partial derivatives
  • Use a partial derivative in applied contexts (local linear approximation)
  • Consult the main points of the lesson

Before class

  • Read Hughes-Hallett 9.3
  • Ponder problems  9.3.1, 2, 6, 10, 12.

In class