Introduction. Roundoff errors and computer arithmetic. Linear systems of equations: Gaussian elimination, LU factorization and Choleski methods. Norms-Stability of linear systems of equations. Jacobi and Gauss–Seidel methods. Eigenvectors and eigenvalues. Method of Least Squares. Interpolation and Fitting: Lagrange and Hermite interpolation. Numerical Integration. Lagrange integration formulas. Gauss integration. Nonlinear equations and systems of equations: bisection method, fixed-point iteration, Newton– Raphson method, etc. Boundary value problems for Ordinary Differential Equations: Taylor and Runge-Kutta methods. Single and multi-step methods. Predictor-Corrector methods. Applications to real world problems.
Written examination at the end of the semester and optional tasks.