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Power_series_function_representation

We already saw how Taylor and Maclaurin series can be used to represent a variety of functions. In this tutorial, we will expand the scope of functions that we can represent with power series, by enriching our toolkit!

Taylor_Maclaurin_polynomials_intro

Taylor polynomials are a very clever way of approximating any function with a polynomial. Maclaurin polynomials are a special class of Taylor polynomials. Learn how these polynomials work in this tutorial.

Challenge_series_exercises

Review you knowledge about series with some challenging exercises.

Maclaurin_series_of_sin_x_cos_x_and_e_

A Maclaurin series is essentially a Maclaurin polynomial with infinite terms. It turns out that the Maclaurin series of sin(x), cos(x), and eˣ return the exact same values as the functions themselves, for any x-value. Wow! Introduce yourselves to these special series and discover one of the most fascinating areas of all of mathematics!

Power_series_intro

Power series is a sum of terms of the general form aₙ(x-a)ⁿ. As you can see, it's actually a function whose sum depends on the x-value. It is a generalization of geometric series, and an extremely useful class of series. Learn more about it in this tutorial.