Numerical Analysis I

Sources of error and conditioning. Solution of algebraic equations in one variable: Bisection method, Fixed point iteration method, Newton’s method and its variants, and their conver-gence. Approximation and interpolation: Monomial and Lagrange interpolations, Newton’s divided difference form, Hermite interpolation, and Cubic spline. Numerical differentiation: Deriving formulas using Taylor series, Truncation error, and Richardson extrapolation.