PH 422 (Vector Fields) Math Bits

Power Series Basics

dr(vector)

Derivatives of Scalar Fields

Divergence (40 min)

Divergence Theorem (20 min)

  • Reading: GVC § Divergence Theorem
  • Derivation of the Divergence Theorem (lecture). We follow “div, grad, curl and all that”, by Schey. The Divergence theorem is almost a lemma based on the definition of divergence. Draw a diagram of an arbitrary volume divided into lots of little cubes. Calculate the sum of all the fluxes out of all the little cubes (isn't this a strange sum to consider!!) and argue that the flux out of one cube is the flux into the adjacent cube unless the cube is on the boundary.

Curl

Stokes' Theorem

Product Rules


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