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What exactly allows a differential relation form of an equation?

  1. Sep 5, 2012 #1
    What exactly allows a "differential relation" form of an equation?

    I understand this in a superficial way but I'd really like some more clarification. If anybody can provide a little better understanding on this subject, please feel free to post anything at all. Even a sentence or two would be helpful.

    I am reading through the optics section of my Stellar Astrophysics book and I came across the following sentences:

    Using the small-angle approximation, tan(θ) ≈ θ, for θ expressed in radians, we find

    y = fθ. ​

    This immediately leads to the differential relation known as the plate scale, dθ/dy,

    [itex]\frac{dθ}{dy}[/itex] = [itex]\frac{1}{f}[/itex].​

    What I don't completely understand is how and why one can simply go from the y=fθ form to the dθ/dy = 1/f form. I understand what the equation means but I don't understand the rules behind switching from one form to the other. Are there any or can I change any two variables to differential form to get a new relation? Any help or guidance at all would be appreciated.
  2. jcsd
  3. Sep 5, 2012 #2
    Re: What exactly allows a "differential relation" form of an equation?

    For f not a function of y or theta,

    dy= fdθ

    Then its just symbol pushing.
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