Math 17

Outline for Exam 3

1. Pre-exam II material

2. Conservative vector fields:

• definition in terms of gradient
• how to find potential function
• fundamental theorem of work integrals
  • statement
  • application to computing line integrals
• closed curves
• independence of path
• notation and when it is appropriate
• conservative vector field theorem

3. Green's Theorem

• statement
• applications

4. Parameterizing surfaces

• scalar and vector form
• important categories
  • function graphs
  • spheres (using q and f)
  • cylinders, parabolas, cones, spheres, etc. (using r and q )
• computation and meaning of

5. Surface integrals

• definition as a limit of Riemann sums
• computation method
  • scalar functions
  • vector fields
• applications to computing
  • surface area
  • mass from density
  • flux

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