Divergence

Learning objectives

  • Compute divergence of a vector field by thinking about mass flow into a box
  • Understand the divergence theorem as giving 2 ways to calculate rate of change of mass inside a box
    • By measuring the flow of mass into the box through all its bounding surface
    • By measuring the rate of change of density of mass at each each point inside the box
  • View divergence as a multiplier
    • Flux of \vec F through the surface of a small box \approx (div \vec F) (Volume of box)
  • Use the divergence theorem
  • Derive the diffusion equation

Before class

  • Read Hughes-Hallett sections 19.3 and 19.4
  • Ponder Hughes-Hallett problems: 19.3: 4, 6, 7, 20; 19.4: 1,3.

In class