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Infinitesimals of order higher

  1. Oct 15, 2013 #1
    in a certain problem it was written Δθ=∂θ/∂x*Δx + ∂θ/∂y*Δy + ∂θ/∂z*Δz + infinitesimals of order higher than Δx,Δy and Δz.can anyone tell me what is "infinitesimals of order higher than Δx,Δy and Δz?"
     
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  3. Oct 15, 2013 #2

    arildno

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    Squares, cubes and so on.

    For "a" tiny, a^2 is even tinier.
     
  4. Oct 15, 2013 #3
    yes but there are no square or cube terms inthe expression
     
  5. Oct 15, 2013 #4

    D H

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    Sure there are. It's the "infinitesimals of order higher than Δx,Δy and Δz". Expanding that Δθ to incorporate some of the second order terms yields

    Δθ = (∂θ/∂x)Δx + (∂θ/∂y)Δy + (∂θ/∂z)Δz
    + (1/2)((∂2θ/∂x2)Δx2 + (∂2θ/∂x∂y2)ΔxΔy + (∂2θ/∂x∂z2)ΔxΔz + (∂2θ/∂y∂x2)ΔyΔx + ∂2θ/∂y2)Δy2 + ···)
    + terms of order three and higher.
     
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