Numerical Methods Guide

A skill for applying numerical methods in scientific computing and research. Covers root finding, numerical integration, ODE solvers, optimization, interpolation, and error analysis with practical implementations in Python.

Root Finding

Newton's Method and Alternatives

import numpy as np


def newton_method(f, df, x0: float, tol: float = 1e-10,
                  max_iter: int = 100) -> dict:
    """
    Newton's method for finding roots of f(x) = 0.