Numericalmethods Stories

This Wattpad mini-book tells the story of how mathematicians learned to measure the "area under a curve" when exact formulas aren't available. It starts by linking integrals to series through Riemann's idea: turning a smooth area into a sum of tiny slices. After a quick look at rectangles and trapezoids (and why straight lines can miss curvature), it introduces the real hero: Simpson's Rule, which fits a parabola through three points to capture the curve's bend and compute the area with surprising accuracy. Along the way, it explains-without heavy theory-how error is estimated (the Lagrange/Taylor intuition), why Simpson's accuracy improves so fast, and how to apply the method in practice with a simple, repeatable workflow and small "quests" to build confidence.