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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

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    Science Advisor

    ANY (modern) text on differential geometry and differentials will deal with those.
     
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