virajdatt / taylor_series_gif

Visualizing Taylor Series approximation as a gif. Learn how to create a gif out of the matplotlib graphs.

taylor_series_gif

Introduction

Inspired from 3Blue1Brown to learn mathematics with vizualization and use these vizualization to better my intutions. I have created this repo which shows how Taylor series approximation gets better with additional degree of polyinomal added (specifically with the cos function as an example). Here I have utilized the python libraries matplotlib (to generate the graphs) and imageio (to create the gif).

Code Details

1. The src folder contains the source code, like the functions used to approximate the value of cos at a given value, plotting various values and creating the gif. The run_approx.py runs these functions implemented in the approx.py file.

2. The tests folder contain a couple of test cases to confirm the code works as expected (TDD).

3. The notebooks folder contains a jupter notebook which shows how to use the functions from src (approx.py) to vizualize things.

Feel free to play around and implement other functions(like sin, e^x) and see how the approxmiations get better.

TO-DO

Show how the Taylor Serier fails to approximate nasty discontinued function f(x) = 1/x when x<0 (As the funtion is undefined at x = 0 and if we start with x=1 we just get the upper right half the graph).