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Thread: Leibniz Notation vs Lagrangian Notation

  1. #1 Leibniz Notation vs Lagrangian Notation 
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    For Leibniz notation, we know what y is differentiated in terms of, e.g. dy/dx. However, for Lagrangian notation it's just y'. How will we know what y is differentiated in terms of for a differential equation like y' + xy = 0?
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    Quote Originally Posted by DataCrusader21 View Post
    For Leibniz notation, we know what y is differentiated in terms of, e.g. dy/dx. However, for Lagrangian notation it's just y'. How will we know what y is differentiated in terms of for a differential equation like y' + xy = 0?
    You know from the equation y' + xy = 0 that y'=dy/dx.

    If you were to look at y' + ty = 0 you would know that y'=dy/dt, no?
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    You learn to read problems, equations and diagrams. You learn it, become familiar with it and it becomes second nature. And sometimes often you scratch your head and say what the %$&?%? is this? And you grunt it out. And sometimes there are two, three or ten of you looking at the same thing trying to interpret the thing. (by then it is usually more than a y' thing.
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    Generally. It's pretty obvious what it means. I cannot recall a situation where I was left in any doubt. Usually thought the dot notation seems to be differentiation wrt to time, but the context makes it obvious in most situations.
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    Quote Originally Posted by x0x View Post
    You know from the equation y' + xy = 0 that y'=dy/dx.

    If you were to look at y' + ty = 0 you would know that y'=dy/dt, no?
    Right. But what about the case where there are more than two variables? I.e. y' + xy + z = 0?
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  6. #6  
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    If in doubt go with differentiation wrt time. Generally though it is pretty obvious in the context. Do you a particular example that is bothering you?
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  7. #7  
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    Quote Originally Posted by DataCrusader21 View Post
    For Leibniz notation, we know what y is differentiated in terms of, e.g. dy/dx. However, for Lagrangian notation it's just y'. How will we know what y is differentiated in terms of for a differential equation like y' + xy = 0?
    It's implied. Note that y' can't be used for a partial derivative. That means that it must be a total derivative with respect to the independent variable. In this case that's x.

    If there are more than two variables then you're not allowed to use the prime notation by convention. You then have to switch to partial derivatives because you've then gone into multivariable analysis in which the differential equations are partial differential equations.
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    Ah thanks, I guess that should had been obvious. Thanks again to everyone!
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  9. #9  
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    Quote Originally Posted by DataCrusader21 View Post
    Ah thanks, I guess that should had been obvious. Thanks again to everyone!
    You're very welcome. That's why we're here. It's a great feeling to know that you've helped somebody out!
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