Make a list of all definitions in the section (a few words each is fine). Summarize any lengthy definitions introduced in this section in your own words.
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linear approximation or tangent line approximation:
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linearization:
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differential - If y=f(x) where f is differentiable, then the
differential dx is an independent variable, and differential dy is related
to it by
We typically think of these differentials as small changes along the tangent line to the graph of f at the point x.
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relative error is the error divided by the value of the function, e.g.
Make a list of all theorems (lemmas, corollaries) in the section (a few words each is fine). Summarize each one introduced in this section in your own words.
None to speak of.
Make a note of any especially useful properties, tricks, hints, or other materials.
Summarize the section in two or three sentences.
We often find it necessary to approximate complicated functions by linear approximations - this simplifies things considerably, but at the cost of introducing errors, of course. It is an approximation, after all.