I. Data fitting: Lagrange interpolation, Chebyshev interpolation, least squares approximation, polynomial regression, orthogonal systems of polynomials (Legendre, Laguerre, Hermite), fast Fourier transform.
II. Numerical integration: Newton-Cotes quadrature, Gauss quadrature (Gauss-Legendre, Gauss-Laguerre, Gauss-Hermite).
III. Iterative methods for solution of nonlinear equations: bisection, fixed-point iterations, Newton method.
IV. Numerical solution to ordinary differential equations: one-step Euler, Crank-Nicholson, and Runge-Kutta methods, multi-step methods, predictor-corrector methods, Galerkin methods, parareal methods.
II. Numerical integration: Newton-Cotes quadrature, Gauss quadrature (Gauss-Legendre, Gauss-Laguerre, Gauss-Hermite).
III. Iterative methods for solution of nonlinear equations: bisection, fixed-point iterations, Newton method.
IV. Numerical solution to ordinary differential equations: one-step Euler, Crank-Nicholson, and Runge-Kutta methods, multi-step methods, predictor-corrector methods, Galerkin methods, parareal methods.