CH02_SEC01_2_Gibbs.ipynb

Kernel: Python 3

import numpy as np
import matplotlib.pyplot as plt
plt.rcParams['figure.figsize'] = [8, 8]
plt.rcParams.update({'font.size': 18})

dx = 0.01
L = 2*np.pi
x = np.arange(0,L+dx,dx)
n = len(x)
nquart = int(np.floor(n/4))

f = np.zeros_like(x)
f[nquart:3*nquart] = 1

A0 = np.sum(f * np.ones_like(x)) * dx * 2 / L
fFS = A0/2 * np.ones_like(f)

for k in range(1,101):
    Ak = np.sum(f * np.cos(2*np.pi*k*x/L)) * dx * 2 / L
    Bk = np.sum(f * np.sin(2*np.pi*k*x/L)) * dx * 2 / L
    fFS = fFS + Ak*np.cos(2*k*np.pi*x/L) + Bk*np.sin(2*k*np.pi*x/L)
    
plt.plot(x,f,color='k',linewidth=2)
plt.plot(x,fFS,'-',color='r',linewidth=1.5)
plt.show()