• Introduction to the Numerical Mathematics,

• Numerical solution of linear equation systems – backward substitution, Gaussian elimination, Gaussian elimination with scaled partial pivoting, Jacobi method, Gauss-Seidel method, Gauss-Jordan method, LU-factorization,

• Eigenvalues – computing the largest eigenvalue,

• Numerical solution of nonlinear equations – root separation, interval splitting, bisection method, Newton’s method, simple iteration method, solution of nonlinear equation systems,

• Interpolation – polynomial approximation of functions, linear interpolation, Lagrange interpolation polynomial, Newton interpolation polynomial, Aitken interpolation, method of least squares,

• Numerical differentiation,

• Numerical integration – rectangle rule, trapezoidal rule, Simpson’s rule,

• Numerical solution of differential equations – Euler method, Predictor-corrector method, Runge-Kutta method.

• Classification of optimization tasks,

• Linear programming,

• Optimization and Game Theory,

• Simplex method,

• Branch and Bound method,

• Dynamic programming a optimization,

• Nonlinear programming,

• One-parameter optimization tasks – golden section search method, Fibonacci search method,

• Multi-parameter optimization tasks – method of least squares (discrete and continuous), gradient method, Cauchy method of steepest descent,

• Constrained optimization tasks – Lagrange method, penalty method.

• Introduction, basic terms,

• Creating and editing simple spreadsheets,

• Usage of functions,

• Usage of mathematical and statistical functions,

• Usage of logical functions,

• Database functions and their properties,

• Usage of filters,

• Creation of charts,

• Partial sums, contingency table, contingency chart,

• Solution of equations, usage of solver,

• Linear regression.