Course 1 Notions of errors theory (Types of errors, Classification, Approximation, Errors, Absolute and Relative Error, Significant digits, propagation of errors in numerical procedures.
Course 2 – Nonlinear equations in real number set (R). Finding roots of nonlinear equation defined as f(x)=0. Bracketing methods: Bisection method.
Course 3 - Nonlinear equations in real number set (R). Finding roots of nonlinear equation defined as f(x)=0. Secant and Regula Falsi method.
Course 4: Nonlinear equations in real number set (R). Finding roots of nonlinear equation defined as f(x)=0. Newton method.
Course 5. Nonlinear equations in real number set (R). Finding roots of nonlinear equation defined as f(x)=0. Finding roots of polynomial equations.
Course 6-7. Nonlinear equations on real number set (R). Finding roots of nonlinear equation defined as x=g(x). Fixed point theorems. "Contractant" applications (functions).
Course 8-9. Nonlinear equations on real number set (R). Fixed point procedures. Modified Newton method. Convergence accelerators.
Course 10. Nonlinear equations on Rn (Nonlinear vectorial equations). Newton's method and descending (gradient) approach.
Course 11. The linear system of equations. Gauss elimination technique.
Course 12. The linear system of equations. Cholesky method. Ill and well-conditioned system of equations.
Course 13. Eigenvalue and eigenvector problems
Course 14. Polynomial interpolations.
