Numerical analysis develops algorithms for solving continuous mathematical problems. It focuses on approximation methods for equations, integrals, and derivatives. Accuracy, stability, and efficiency are key considerations. Techniques include root-finding, interpolation, and numerical integration. Error analysis quantifies the accuracy of approximations. Numerical linear algebra solves large systems of equations and eigenvalue problems. Numerical methods are essential in science, engineering, and finance. They enable computer simulations of complex phenomena, from weather prediction to structural analysis. Numerical analysis bridges the gap between theoretical mathematics and practical computation, providing tools to approximate solutions where exact solutions are intractable.