Figure 2.5:

Truncated trigonometric Fourier series approximation to f(x)=x, using K=5,10, 50. The wiggles get finer as K increases.

Code for Figure 2.5

Text of the GNU GPL.

main.py

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import numpy as np
import matplotlib.pyplot as plt

nxs = 301
x = np.linspace(-np.pi, np.pi, nxs)
nterms = [5, 10, 50]
u = np.zeros((len(nterms), nxs))

for i, nterm in enumerate(nterms):
    for k in range(1, nterm + 1):
        sign = (-1) ** k
        un0 = -2 * sign / k
        u[i, :] += un0 * np.sin(k * x)

plt.plot(x, u.T)
plt.show(block=False)

with open("Fourierx.dat", "w") as f:
    np.savetxt(f, np.column_stack([x, *u]), fmt="%f")