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In physics, there appear a type of equations following this format,

$ Q2 = Q1(1 + a \Delta T) $

Where Q1 is the first quantity

Q2 is the changed quantity,

a is the changing coefficient,

$ \Delta T $ is the change of the factor (for example, temperature)

They appear in equations on resistance, expansion etc.

Deriving them are simple, But what I like to know is what this type of relations are called in general.

Thanks.

Edit: with T I meant a change, so i've added a Delta for it as pointed out in the comments.

practronix512
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1 Answers1

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Let $q2=y,dT=x $(for small interval) since $q1,a $ are constant then equation is $y=q1+mx $ where $m=q1a $ thus the equation is a linear approximation for a function when $x $ is very very small.

Archis Welankar
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    Within the context of the problem, I'd say that such a relation is a linear approximation of how the dependent variable depends on the independent variable: a small change in the independent variable should produce a proportional small change in the dependent variable. One does not expect it to hold for large changes; for instance, the resistance won't vary linearly with temperature if the material gets so hot that it melts! – Semiclassical May 31 '17 at 17:52
  • So that T should be simply dT so that we can say its a linear approximation – Archis Welankar May 31 '17 at 18:03
  • Well, the OP does label T as a change, not as the independent variable itself. But $\Delta T$ is better notation regardless. – Semiclassical May 31 '17 at 18:05
  • $ \Delta T $ is not very very small sometimes! We can have 100 in it to present 100 celcius change. But anyway, thanks for your help! – practronix512 Jun 01 '17 at 04:41