Editing Numerical Methods (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Modeling 'Root Finding' (Newton's Method):'''
<syntaxhighlight lang="python">
def find_root_newton(func, deriv, start_x):
    """
    Finds where func(x) == 0.
    """
    x = start_x
    for i in range(10): # 10 Iterations
        # Newton's Formula: x_next = x - f(x)/f'(x)
        x = x - (func(x) / deriv(x))
        print(f"Iteration {i+1}: x = {x:.6f}")
    return x

# Find the square root of 2 (i.e. solve x^2 - 2 = 0)
f = lambda x: x**2 - 2
df = lambda x: 2*x
print(f"Final Approximation: {find_root_newton(f, df, 1.5)}")
# Note how it hits the 'Exact' answer incredibly fast.
</syntaxhighlight>

; Numerical Toolkits
: '''Finite Element Analysis (FEA)''' → Breaking a car or bridge into millions of tiny "Elements" to see where it will break.
: '''Monte Carlo Simulation''' → Solving a problem by running 1,000,000 random "What if" scenarios (used in finance and physics).
: '''Fast Fourier Transform (FFT)''' → The algorithm that converts sound waves into digital data (mp3s/phone calls).
: '''PageRank''' → The numerical method Google uses to solve the "Web Importance" matrix.
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