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Category Archives: Power Series
Taylor Series Uses #1: Complicated Integrals
1. Can you compute ? Well, first we consider the antiderivative for …which doesn’t exist. What do we do? Cry. No, what I mean is, use Taylor series!
Posted in Analysis, Calculus, Infinite Series, Power Series, Taylor Series
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Taylor Polynomials
1. So last time we concluded discussing Taylor series with constructing a polynomial using the first terms in the Taylor series. This “Taylor polynomial” approximated our function, and we want to know how well does it approximate? We will derive … Continue reading
Posted in Analysis, Calculus, Differential, Infinite Series, Power Series, Taylor Series
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Taylor Series
0. Can we approximate a function using a power series? With the calculus’ help, we can!
Posted in Analysis, Approximation, Calculus, Differential, Infinite Series, Power Series, Taylor Series
Tagged Power Series, Taylor Series
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Power Series
1. Definitions. Let be a variable. a series of the form (1) is called a “Power Series about ”. A series of the form (2) is called a “Power Series about ”. Example 1. Consider the series (3) For what … Continue reading