Editing Temperature coefficient (section)

==Mathematical derivation of temperature coefficient approximation==
In its more general form, the temperature coefficient differential law is:
:<math>\frac{dR}{dT} = \alpha\,R</math>

Where is defined:
:<math>R_0 = R(T_0)</math>

And <math>\alpha</math> is independent of <math>T</math>.

Integrating the temperature coefficient differential law:
:<math>
       \int_{R_0}^{R(T)}\frac{dR}{R} = \int_{T_0}^{T} \alpha\,dT ~\Rightarrow~
       \ln(R)\Bigg\vert_{R_0}^{R(T)} = \alpha(T - T_0) ~\Rightarrow~
  \ln\left( \frac{R(T)}{R_0} \right) = \alpha(T - T_0) ~\Rightarrow~
                                R(T) = R_0 e^{\alpha(T-T_0)}
</math>

Applying the [[Taylor series]] approximation at the first order, in the proximity of <math>T_0</math>, leads to:
:<math>R(T) = R_0(1 + \alpha(T - T_0))</math>