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1. Mathematical analysis: Numeric sequences; Real topology; Metric spaces; Differential calculus of functions of one or n variables: Limit and continuity, differentiation, partial derivatives, curves and surfaces; Integral calculus: integral of functions of one variable, multiple integrals, curvilinear integrals, surface integrals; Differential forms: integral formulas of the mathematical analysis (Green formula, Stokes formula, Gauss-Ostrogradskii formula); Optimization of functions of n variables.

2. Series and Integrals: Numeric series; Functional sequences and functional series; Power series; Taylor series; Fourier series and Fourier integrals; Fourier transformations; Laplace transformation; Improper integrals; Integral depending on parameters.

3. Differential equations: Ordinary differential equations: method on integration of ODEs, quantitative and qualitative studies of ODE, Existence and uniqueness of solutions of Cauchy problem, boundary value problems for ODE; Stability of solutions; Dynamic systems. Partial differential equations: Classification of quasilinear partial differential equations; Fundamental equations of the mathematical physics; Wave equations; Heat equations; Laplace equations; Potential theory; Boundary and initial value problems for PDE; Fourier solutions, Poisson solutions, and D’Alembert solutions of boundary and initial problems for PDE.

4. Special function of mathematical physics: Bessel equations and Bessel functions; Legendre equations and Legendre functions; Laguerre equations and Laguerre functions; Spherical functions; Applications to the study of particles movement.

5. Numerical methods: Numerical resolution of algebraic equations; Numerical integration; Numerical differentiation; Polynomial interpolation; Numerical resolution of Cauchy problem for ODE.

6. Optimization and linear programming: Convex analysis; Linear programming with constraints; Linear programming without constraints; The simplex algorithm; Nonlinear optimization; discrete programming; Optimization with constraints; Optimization without constraints.

7. Mathematics for engineering: Mathematics for computer Sciences; Mathematics for Live Sciences.