Taylor Series App

A handy tool to demonstrate taylor series expansions

Taylor Series Quick Overview

  • Taylor series expansions are used to approximate the values of functions around a particular, predefined point.
  • The Maclaurin Series is the Taylor Series expansion around the point x = 0.
  • The more terms you include in the Taylor series estimate the closer the approximation but the longer it takes to compute.
  • Taylor series expansions are widely used in the scientific computing arena to numerically find the solutions for Differnetial and Partial Differential equations. In fact the well known Runge Kutta technique for finding the numerical solution for differential equations is actually derived from Taylor Series expansions!
  • Ever wondered how your computer figures out the values of sin, cos, exp, tan, and logorithms?

The Pitch

Given all the great things that we use Taylor Series expansions for wouldn't it be great if you had an app that could demonstrate the effect of including more or less terms to students? Well your wait is over.

Head over to https://rmclaren.shinyapps.io/Project/ where you can start playing with Taylor Series today!

App Description

  • The App lets users choose to play with taylor expansions for sin(x), tan(x) and ex.
  • The number of terms from 1 to 10 can be picked and the plot will immediatly update showing the plot of the Taylor Series expansion (in red) superimposed over the function that is being approximated.

In Conclusion