Numerical Derivatives

Goals: Recognize the first-order forward and first order backwords difference method for approximating a derivative

use python to implement a given finite difference scheme calculation for approximating the derivative of a function at a particular point

use a for loop or slicing to approximate a derivative on a grid (discretization)

example

we want to approximate f’(3) for the function f(x) = 2x + cos(x)

using the first order forward difference formula

change of x = 0.1

$f^{\prime}\left(3\right)=\frac{f\left(3+0.1\right)-f\left(3\right)}{0.1}$

code:

import numpy as np

def f(x):

    return 2*x + np.cos(x)

deriv = (f(3+0.1) - f(3))/0.1

print(f”f’(3) approximately equals {deriv}”)

^^ that was an example of a def function but there is an easier way called annonymous functions

import numpy as np

f = lambda x: 2*x + np.cos(x)

deriv = (f(3+0.1) - f(3)) / 0.1