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 through the surface of a small box (div ) (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

• Notes on the divergence theorem
• More information in  section 1 of document on fluid mechanics
• Problems on divergence and divergence theorem