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Math Help - Mathematical models

  1. #1
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    Mathematical models

    Hi,

    I have problem understanding about mathematical models used for analysis of particular system. Thing is that i understand derivatives and integretion (i mean in math level). But i don't understand how it is related to those mathematical models. As much as I understand its like, when u have some kind mathematical model for system, and its result varies non-linear in meter of time, so when you write derevative of that model, you get approximation, which now is linear. Am i right?

    Lets say I got task:

    A thermistor has a response to temperature represented by R=R0 * e^-0.01*T, where R0=10000, R=resistance, and T=temp. in degree Celsius. Find the linear model for the thermistor operating at T=20 C, and for a range of variation of temperature.

    I think when T=20, you just have to put it into equation, and then you will get result, which depicted on the graph would look like stright curve? About second part solution I have no clue...
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by bishop View Post
    Hi,

    I have problem understanding about mathematical models used for analysis of particular system. Thing is that i understand derivatives and integretion (i mean in math level). But i don't understand how it is related to those mathematical models. As much as I understand its like, when u have some kind mathematical model for system, and its result varies non-linear in meter of time, so when you write derevative of that model, you get approximation, which now is linear. Am i right?

    Lets say I got task:

    A thermistor has a response to temperature represented by R=R0 * e^-0.01*T, where R0=10000, R=resistance, and T=temp. in degree Celsius. Find the linear model for the thermistor operating at T=20 C, and for a range of variation of temperature.

    I think when T=20, you just have to put it into equation, and then you will get result, which depicted on the graph would look like stright curve? About second part solution I have no clue...
    i don't get it either, if we set the temperature to 20 C, then it is not varying, it is stuck at 20 C, what range are we looking for?
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  3. #3
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    as much as i understand its smth like from t0 to infinity. I think, range does not mater, if that is model.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by bishop View Post
    Hi,

    I have problem understanding about mathematical models used for analysis of particular system. Thing is that i understand derivatives and integretion (i mean in math level). But i don't understand how it is related to those mathematical models. As much as I understand its like, when u have some kind mathematical model for system, and its result varies non-linear in meter of time, so when you write derevative of that model, you get approximation, which now is linear. Am i right?

    Lets say I got task:

    A thermistor has a response to temperature represented by R=R0 * e^-0.01*T, where R0=10000, R=resistance, and T=temp. in degree Celsius. Find the linear model for the thermistor operating at T=20 C, and for a range of variation of temperature.

    I think when T=20, you just have to put it into equation, and then you will get result, which depicted on the graph would look like stright curve? About second part solution I have no clue...
    The derivative gives the slope of a function at a point. Now for a smooth function near the point the function looks like a straight line. So we have:

    f(x)\approx f(x_0)+(x-x_0)f'(x_0)

    for x close to x_0, that is all that a linearization of a model is doing, there is no great mystery its just a property of differentiable functions.

    RonL
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  5. #5
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    Quote Originally Posted by CaptainBlack View Post
    The derivative gives the slope of a function at a point. Now for a smooth function near the point the function looks like a straight line. So we have:

    f(x)\approx f(x_0)+(x-x_0)f'(x_0)

    for x close to x_0, that is all that a linearization of a model is doing, there is no great mystery its just a property of differentiable functions.

    RonL
    Can you explain for a person that understands just derivatives, integration, and physics. How for example write model of current change in meter of time in RLC circuit:

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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    The derivative gives the slope of a function at a point. Now for a smooth function near the point the function looks like a straight line. So we have:

    f(x)\approx f(x_0)+(x-x_0)f'(x_0)

    for x close to x_0, that is all that a linearization of a model is doing, there is no great mystery its just a property of differentiable functions.

    RonL
    i thought they were after something like that. but when they gave a specific value for T it threw me off.
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