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Old   July 27, 2004, 02:48
Default Taylor series expansion
Joe cool
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Hi all,

May I know for a 3D Taylor series expansion, is it like this:

f1 = f0 + delx*fx + dely*fy + delz*fz + 0.5*delx*delx*fxx + 0.5*dely*dely*fyy + 0.5*delz*delz*fzz + delx*dely*fxy + delx*delz*fxz + dely*delz*fyz + 1/6 delx^3 fxxx + 1/6 dely^3 fyyy + 1/6 delz^3 fzzz + 0.5*delx*delx*dely*fxxy + 0.5*delx*dely*dely*fxyy + 0.5*delx*delx*delz*fxxz + 0.5*delx*delz*delz*fxzz + 0.5*dely*dely*delz*fyyz + 0.5*dely*delz*delz*fyzz + delx*dely*delz*fxyz

where delx = x(1)-x(0), dely = y(1)-y(0), delz = z(1)-z(0),

fx= df/dx, fxx= d^2/dx^2 (second derivative), etc...

Is the expression correct? I can't seem to verify this anywhere...
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Old   July 27, 2004, 03:46
Default Re: Taylor series expansion
Junseok Kim
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You can use Mathematica software to calculate it. Try this.

Series[f[x, y, z], {x, x1, 3}, {y, y1, 3}, {z, z1, 3}]

where (x1,y1,z1) is a point which you want to expand the function and 3 is the order of the polynomial.

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