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

  • #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:

Answers and Replies

  • #2
HallsofIvy
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ANY (modern) text on differential geometry and differentials will deal with those.
 

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