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! Advertisements

Posted in Analysis, Calculus, Infinite Series, Power Series, Taylor Series | Leave a comment

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 | Leave a comment

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 , | 3 Comments

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

Posted in Analysis, Calculus, Infinite Series, Power Series | Tagged | Leave a comment