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