Section 8.2 Power Series and Analytic Functions
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objective
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to be able to
determine the convergence set of power series
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to be able to
perform arithmetic operations of power series
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to be able to
find power series expansions for f'(x) and the integral of f(t)dt
evaluated from 0 to x, given f(x)
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to be able to
change the index variables in summations
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to be able to
determine Taylor series of a given function from other similar series
key ideas and/or vocabulary
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power series
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converges/diverges
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converges absolutely
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radius of convergence
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Ratio test
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harmonic series
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alternating series
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Cauchy product
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differentiation and integration of power series
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analytic function
solved problems - using key ideas
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finding the convergence set of a power series, #5
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arithmetic operations with power series, #9,11
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finding power series expression for f'(x),
given f(x), #19,21
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change of index variables, #23
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determining the Taylor series about the point x0