Local linearity

Learning objectives

  • Use differentials to make linear approximations: 
    • \Delta f \approx f_x \Delta x + f_y \Delta y for small \Delta x and \Delta y
  • Use gradients to make linear approximations:
    • \Delta f \approx (\hbox{grad }f) \cdot \Delta \vec r for small \Delta \vec r = \Delta x \vec i + \Delta y \vec j
  • Use the gradient to compute directional derivatives
  • Understand the geometry of the gradient

Before class

  • Read Hughes-Hallett sections 14.3, 14.4, 14.5.
  • Ponder Hughes-Hallett problems: 14.3: 7, 17, 18, 24, 26; 14.4: 1, 2, 7, 17, 23, 32-3; 14.5: 33, 49.

In class

On your own

Advertisements