# Science:Infinite Series Module/Units/Unit 3/3.2 Taylor Series

## What This Lesson Covers

In this lesson we will introduce a few concepts:

- representation of functions with a power series
- conditions for convergence of a power series
- radius of convergence of a power series

## Learning Objectives

After reading this lesson and completing a sufficient number of exercices on paper, you should be able to

- expand a given function in a Maclaurin series
- determine the radius of convergence of a Taylor series

## Topics

- A motivating problem
- The Taylor and Maclaurin expansions
- The Maclaurin expansion of
*e*^{x} - The Maclaurin expansion of sin(
*x*) - The Maclaurin expansion of cos(
*x*) - A list of Maclaurin expansions
- Videos on Taylor Series