[Math]Gradient, curl, divergence

. dot product(inner product)
  . http://en.wikipedia.org/wiki/Dot_product
  . (vector * vector) -> scalar
  . lengths and angles (projection)
  . a.b = |a||b|cos(theta)

. cross product(outer product)
  . vector * vector -> vector
  . area of parallelogram, perpendicular
  . a x b = n|a||b|sin(theta)

. Scalar triple product
  . http://en.wikipedia.org/wiki/Triple_product
  . V = |a.(bxc)|

. Vector triple product
  . ax(bxc)

. del
  . differential operator del
  . nabla(역삼각형 모양)
   http://en.wikipedia.org/wiki/Nabla_symbol

. flux
  . http://en.wikipedia.org/wiki/Flux
  . the magnitude of a river's current
  . the amount of water that flows through a cross-section of the river each second

. Gradient
  . http://en.wikipedia.org/wiki/Gradient
  . Measure of the slope(steepness, fall, incline) of a straight line
  . Whose magnitude is the greatest rate of change
  . the direction of the greatest rate of increase of the scalar field
  . f(x) : scalar function (vector -> scalar)
  . x : vector variable
  . grad(f) = (af/ax1, ... af/axn) : (vector -> scalar) -> vector
  . a : partial derivatives
  . invariant under orthogonal transformations

. Divergence
  . F = (F1, F2, .. Fn)
  . div F : (aF1/ax1 + aF2/ax2 + .. + aFn/xn) : vector -> scalar
  . div = nabla inner-product
  . linear operator
  . vector field's tendency to originate from or converge upon a give point
  . flux density
  . derivative of the net flow of the vector field
  . div F(x0, y0) > 0 : source, expand
  . div F(x0, y0) < 0 : sink, shrink

. Curl
  . http://en.wikipedia.org/wiki/Curl
  . vector operator
  . F : vector
  . curl(F) : vector -> vector
  . curl = nable cross-product
  . vector fields's rate of rotation
  . the direction of the axis of rotation
  . the magnitude of the rotation
  . circulation density