Numerical differentiation with Python. Border problem

In this video I will show how to do numerical differentiation with Python (NumPy). I will explain, how to make numerical differentiation and what information you need to have to write your first program for calculating derivative.
For the this example, I will calculable derivative for f(x) = sin(x).
Also I will explain, what is the border problem for differentiation and how to describe your domain for calculating.
This short tutorial about numerical differentiation will be good enough to write first simplest code to find derivative of a differentiable functions.
Video content:
0:00 – Intro
0:05 – Graphical definition of derivatives
0:54 – Derivative as a limit
1:16 – First border problem
2:05 – Description of a domain for derivative calculation
3:06 – Coding of our program:
3:40 – Domain coding
5:34 – Calculating sin(x) for differentiation
6:23 – Calculating theoretical derivative for comparison
6:50 – Calculating numerical derivative with NumPy
8:07 – Compare theoretical and numerical results
8:43 – Performance optimization

#derivative #numericalsolution #pythoncoding