Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Higher order differentials: dZ, d^2Z, d^3Z

  1. Mar 30, 2012 #1
    Any books discussing the formula of [itex]d^2Z[/itex] and [itex]d^3Z[/itex]?
    Are they liked that? Anyone saw them before?

    [itex]Z(x, y)\\\\dZ=Z_xdx+Z_ydy\\d^2Z=Z_{xx}(dx)^2+2Z_{xy}dxdy+Z_{yy}(dy)^2+Z_xd^2x+Z_yd^2y\\d^3Z=Z_{xxx}(dx)^3+3Z{xxy}(dx
    )^2(dy)+3Z_{xyy}(dx)(dy)^2+Z_{yyy}(dy)^3+3[Z_{xx}(dx)(d^2x)+Z_{xy}(dxd^2y+d^2xdy)+Z_{yy}(dy)(d^2y)]+Z_xd^3x+Z_yd^3y[/itex]
     
    Last edited: Mar 30, 2012
  2. jcsd
  3. Mar 30, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    ANY (modern) text on differential geometry and differentials will deal with those.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Higher order differentials: dZ, d^2Z, d^3Z
  1. Treating d (Replies: 3)

  2. D and ∂ (Replies: 14)

Loading...