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Finds real roots of f(x) = 0 using symbolic derivatives and quadratic convergence.
Finds root in interval [a, b] where f(a) and f(b) have opposite signs.
Secant line interpolation method to find roots within interval [a, b].
Solves x = g(x) iteratively starting from initial guess x0.
Equal interval interpolation formula using forward difference table Δy for target X near table start.
Equal interval backward difference formula using ∇y for target X near table end.
Unequal interval polynomial interpolation formula for arbitrary (x_i, y_i) data points.
Unequal interval divided difference interpolation for arbitrary tabulated points.
Approximates definite integral ∫[a,b] f(x) dx using N trapezoidal subintervals.
Quadratic parabolic interpolation for integration over even N subintervals.
Cubic interpolation for numerical integration where subintervals N is a multiple of 3.
Solves first order ODE dy/dx = f(x, y) starting at (x0, y0) with step size h.
High accuracy 4th order numerical solution for initial value differential equation dy/dx = f(x, y).
Tests mean difference for large samples (N ≥ 30) with population standard deviation σ.
Tests mean difference for small samples (N < 30) where population standard deviation is unknown.
Tests goodness of fit between observed frequencies O_i and expected frequencies E_i.