1. ## 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?

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...

2. Originally Posted by bishop
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?

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?

3. as much as i understand its smth like from t0 to infinity. I think, range does not mater, if that is model.

4. Originally Posted by bishop
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?

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:

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

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

RonL

5. Originally Posted by CaptainBlack
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:

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

for $\displaystyle x$ close to $\displaystyle x_0$, 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:

6. Originally Posted by CaptainBlack
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:

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

for $\displaystyle x$ close to $\displaystyle x_0$, 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.