Introduction to Taylor and Maclaurin Series

Welcome to the first post of our series on Taylor and Maclaurin series!

What are Taylor and Maclaurin series?

In calculus, Taylor and Maclaurin series are mathematical tools used to approximate functions using infinite series. They are named after mathematicians Brook Taylor and Colin Maclaurin, who made significant contributions to the development of these series.

Significance in calculus

Taylor and Maclaurin series play a crucial role in calculus as they enable us to approximate complex functions with simpler polynomial expressions. These series are particularly useful when it comes to evaluating functions at specific points, calculating derivatives, finding solutions to differential equations, and understanding the behavior of functions.

Topics to be covered

In this series, we will cover the following topics:

1. Understanding power series
2. The Taylor series expansion
3. Deriving Taylor series using Maclaurin series
4. Applications of Taylor and Maclaurin series

So let's get started with our first topic: understanding power series.

Stay tuned for our next post where we delve into the concept of power series, its convergence and divergence, and the notion of radius of convergence.