Week 1 Mathematical Preliminaries Flashcards
what does the grad operator produce
a vector that points to the local maxima
what does the div operator produce
a scalar
what words describe positive and negative divergence
positive called a source
negative called a sink
what does the curl operator produce
a vector
if curl = 0 what can be said
the quantity is conserved
what are the two curl/div/grad identities
curl of grad is always 0
div of curl is always 0
state in words the divergence theorem
the volume integral of div of v = the enclosed area integral of v
state in words the stokes theorem
the area integral of the curl of v = enclosed line integral of v
what does the Dirac delta function allow us to do
model a point charge distribution as a collection of points
what is Poisson’s equation and the special condition for Laplace
∇^2f = -4πg
Special condition for laplace is g = 0
