Perplexed
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I have been looking at material properties such as thermal expansion of metals which usually involves very small coefficients. The general equation of thermal expansion is usually
[math]L_\theta = L_0 ( 1 + \alpha \theta)[/math]
where L is the length and theta is the temperature change. The coefficient alpha is usually pretty small, 11E-6 for steel, so one ends up with a lot of numbers like 1.000011.
This is where I seem to have entered a strange world, where
[math]\sqrt{(1 + x)} \rightarrow 1 + x/2[/math]
[math]\dfrac{1}{ \sqrt{(1 - x)}} \rightarrow 1 + x/2[/math]
[math](1 - x)^3 \rightarrow 1-3x[/math]
Is there a name for this area of maths, and somewhere I can look up more about it?
Thanks for any help.
Perplexed
[math]L_\theta = L_0 ( 1 + \alpha \theta)[/math]
where L is the length and theta is the temperature change. The coefficient alpha is usually pretty small, 11E-6 for steel, so one ends up with a lot of numbers like 1.000011.
This is where I seem to have entered a strange world, where
[math]\sqrt{(1 + x)} \rightarrow 1 + x/2[/math]
[math]\dfrac{1}{ \sqrt{(1 - x)}} \rightarrow 1 + x/2[/math]
[math](1 - x)^3 \rightarrow 1-3x[/math]
Is there a name for this area of maths, and somewhere I can look up more about it?
Thanks for any help.
Perplexed