Numerička integracija

In next video lecture we will say something about error that we make when we use Newton-Cotes formulas

from IPython.lib.display import YouTubeVideo
vid = YouTubeVideo("mjPBinappuI")
display(vid)

In the next part of the lecture we introduce composite numerical integration formulas and the error estimate for these formulas

vid = YouTubeVideo("9_E01OBrzbA")
display(vid)

Exercises

In the next part of the lecture we solve some problems related to numerical integration.

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Implementation of composite integration formulas

def trapez(f,a,b,N=50):
    x = np.linspace(a,b,N+1) 
    y = f(x)
    y_right = y[1:] # lijevi rub intervala
    y_left = y[:-1] # desni rub intervala
    h = (b - a)/N
    Tn = np.sum(h*(y_right + y_left)/2)
    return Tn

import numpy as np
from numpy import exp
from numpy import cos
from numpy import pi

trapez(lambda x : x*exp(-x)*cos(2*x),0,2*pi,6)

-0.2269939761611912

For homework, try to implement the composite rectangular formula and the composite Simpson formula, following the example in the code above !!