# Mathematical models

• Oct 1st 2008, 09:51 AM
bishop
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...
• Oct 1st 2008, 10:02 AM
Jhevon
Quote:

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?
• Oct 1st 2008, 10:08 AM
bishop
as much as i understand its smth like from t0 to infinity. I think, range does not mater, if that is model.
• Oct 1st 2008, 10:09 AM
CaptainBlack
Quote:

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:

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

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
• Oct 1st 2008, 10:25 AM
bishop
Quote:

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:

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

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:

http://www.mm2.lt/rlc.JPG
• Oct 1st 2008, 10:33 AM
Jhevon
Quote:

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:

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

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.