University of Architecture, Civil Engineering and Geodesy (UACEG)

Elements of probability theory are studied: random variable, arithmetic mean, dispersion, co-variation and coefficient of correlation. Basic methods of mathematical statistics are presented - point-wise estimates, maximum like-hood method, test of hypothesis.

Numerical and functional series with real and complex members are considered. Taylor series expansions are obtained for the elementary functions. Solutions of partial differential equations are constructed by using Fourier series. Elements of approximate calculus are presented: approximation of a function, discretization of a continuous problem, construction of an iterative scheme. Fundamentals of the theory of complex functions (continuity, derivatives, integrals) as well as of the probability ...

Numerical and functional series with real and complex members are considered. Taylor series expansions are obtained for the elementary functions. Solutions of partial differential equations are constructed by using Fourier series. Elements of approximate calculus are presented: approximation of a function, discretization of a continuous problem, construction of an iterative scheme. Fundamentals of the theory of complex functions (continuity, derivatives, integrals) as well as of the probability ...

Numerical and functional series with real and complex members are considered. Taylor series expansions are obtained for the elementary functions. Solutions of partial differential equations are constructed by using Fourier series. Elements of approximate calculus are presented: approximation of a function, discretization of a continuous problem, construction of an iterative scheme. Fundamentals of the theory of complex functions (continuity, derivatives, integrals) as well as of the probability ...

Numerical and functional series with real and complex members are considered. Taylor series expansions are obtained for the elementary functions. Solutions of partial differential equations are constructed by using Fourier series. Elements of approximate calculus are presented: approximation of a function, discretization of a continuous problem, construction of an iterative scheme. Fundamentals of the theory of complex functions (continuity, derivatives, integrals) as well as of the probability ...

Numerical and functional series with real and complex members are considered. Taylor series expansions are obtained for the elementary functions. Solutions of partial differential equations are constructed by using Fourier series. Elements of approximate calculus are presented: approximation of a function, discretization of a continuous problem, construction of an iterative scheme. Fundamentals of the theory of complex functions (continuity, derivatives, integrals) as well as of the probability ...

Numerical and functional series with real and complex members are considered. Taylor series expansions are obtained for the elementary functions. Solutions of partial differential equations are constructed by using Fourier series. Elements of approximate calculus are presented: approximation of a function, discretization of a continuous problem, construction of an iterative scheme. Fundamentals of the theory of complex functions (continuity, derivatives, integrals) as well as of the probability ...

Numerical and functional series with real and complex members are considered. Taylor series expansions are obtained for the elementary functions. Solutions of partial differential equations are constructed by using Fourier series. Elements of approximate calculus are presented: approximation of a function, discretization of a continuous problem, construction of an iterative scheme. Fundamentals of the theory of complex functions (continuity, derivatives, integrals) as well as of the probability ...

Numerical and functional series with real and complex members are considered. Taylor series expansions are obtained for the elementary functions. Solutions of partial differential equations are constructed by using Fourier series. Elements of approximate calculus are presented: approximation of a function, discretization of a continuous problem, construction of an iterative scheme. Fundamentals of the theory of complex functions (continuity, derivatives, integrals) as well as of the probability ...

Mathematical economics deals with the analytical and mathematical aspects of the modern economic theory. The course will be an introduction to financial mathematics. Market dynamics, such as trade, loans, interests and control of financial resources is studied. The main mathematical tool will be operational research (linear, nonlinear and dynamical programming as well as the game theory) and elementary mathematical statistics.

The concepts of vectors and matrices are introduced together with the corresponding operations, as well as important scalar functions of vectors and matrices (scalar product, norm, determinant ). Properties of vector spaces are considered. Linear algebraic equations and least-squares problems are studied together with methods for their solution. The eigenstructure (eigenvalues and eigenvectors/associated vectors) of a square matrix is considered as well as methods for its computation. ...

The concepts of vectors and matrices are introduced together with the corresponding operations, as well as important scalar functions of vectors and matrices (scalar product, norm, determinant ). Properties of vector spaces are considered. Linear algebraic equations and least-squares problems are studied together with methods for their solution. The eigenstructure (eigenvalues and eigenvectors/associated vectors) of a square matrix is considered as well as methods for its computation. ...

The concepts of vectors and matrices are introduced together with the corresponding operations, as well as important scalar functions of vectors and matrices (scalar product, norm, determinant ). Properties of vector spaces are considered. Linear algebraic equations and least-squares problems are studied together with methods for their solution. The eigenstructure (eigenvalues and eigenvectors/associated vectors) of a square matrix is considered as well as methods for its computation. ...

The concepts of vectors and matrices are introduced together with the corresponding operations, as well as important scalar functions of vectors and matrices (scalar product, norm, determinant ). Properties of vector spaces are considered. Linear algebraic equations and least-squares problems are studied together with methods for their solution. The eigenstructure (eigenvalues and eigenvectors/associated vectors) of a square matrix is considered as well as methods for its computation. ...

Three main topics are studied: Linear Algebra in n-dimensional space, Analytical Geometry, and Spherical Trigonometry. The concepts of matrices, determinants and n-dimensional vectors are introduced. Linear objects (straight lines and planes, as well as curves and surfaces of second degree) are studied. The main concepts and formulae of the Spherical Trigonometry are considered.

Three main topics are studied: Linear Algebra in n-dimensional space, Analytical Geometry, and Spherical Trigonometry. The concepts of matrices, determinants and n-dimensional vectors are introduced. Linear objects (straight lines and planes, as well as curves and surfaces of second degree) are studied. The main concepts and formulae of the Spherical Trigonometry are considered.

Three main topics are studied: Linear Algebra in n-dimensional space, Analytical Geometry, and Spherical Trigonometry. The concepts of matrices, determinants and n-dimensional vectors are introduced. Linear objects (straight lines and planes, as well as curves and surfaces of second degree) are studied. The main concepts and formulae of the Spherical Trigonometry are considered.

The sets of real and complex numbers are considered. Functions of one and several real arguments are defined. Numerical sequences and the basic elementary functions are studied. The properties of continuability and differentiability of real functions are introduced. An algorithm is presented for the analysis of a real function of one real argument. Primitives and definite integrals are introduced based on the concept of Newton's integral. Applications of derivatives and integrals to geometry, ...

The sets of real and complex numbers are considered. Functions of one and several real arguments are defined. Numerical sequences and the basic elementary functions are studied. The properties of continuability and differentiability of real functions are introduced. An algorithm is presented for the analysis of a real function of one real argument. Primitives and definite integrals are introduced based on the concept of Newton's integral. Applications of derivatives and integrals to geometry, ...

The sets of real and complex numbers are considered. Functions of one and several real arguments are defined. Numerical sequences and the basic elementary functions are studied. The properties of continuability and differentiability of real functions are introduced. An algorithm is presented for the analysis of a real function of one real argument. Primitives and definite integrals are introduced based on the concept of Newton's integral. Applications of derivatives and integrals to geometry, ...

The sets of real and complex numbers are considered. Functions of one and several real arguments are defined. Numerical sequences and the basic elementary functions are studied. The properties of continuability and differentiability of real functions are introduced. An algorithm is presented for the analysis of a real function of one real argument. Primitives and definite integrals are introduced based on the concept of Newton's integral. Applications of derivatives and integrals to geometry, ...

The sets of real and complex numbers are considered. Functions of one and several real arguments are defined. Numerical sequences and the basic elementary functions are studied. The properties of continuability and differentiability of real functions are introduced. An algorithm is presented for the analysis of a real function of one real argument. Primitives and definite integrals are introduced based on the concept of Newton's integral. Applications of derivatives and integrals to geometry, ...

The sets of real and complex numbers are considered. Functions of one and several real arguments are defined. Numerical sequences and the basic elementary functions are studied. The properties of continuability and differentiability of real functions are introduced. An algorithm is presented for the analysis of a real function of one real argument. Primitives and definite integrals are introduced based on the concept of Newton's integral. Applications of derivatives and integrals to geometry, ...

The sets of real and complex numbers are considered. Functions of one and several real arguments are defined. Numerical sequences and the basic elementary functions are studied. The properties of continuability and differentiability of real functions are introduced. An algorithm is presented for the analysis of a real function of one real argument. Primitives and definite integrals are introduced based on the concept of Newton's integral. Applications of derivatives and integrals to geometry, ...

Some classes of ordinary differential equations (ODE) are studied. General and partial solutions of linear ODE in scalar and vector form are constructed. Boundary value problems and eigenstructure problems for linear ODE of second order are considered. Basic facts about curves and surfaces are given. Multiple integrals as well as integrals on curves and surfaces are introduced and their interrelations are studied (Green's formula). Applications of these integrals to mechanics and physics are ...

Some classes of ordinary differential equations (ODE) are studied. General and partial solutions of linear ODE in scalar and vector form are constructed. Boundary value problems and eigenstructure problems for linear ODE of second order are considered. Basic facts about curves and surfaces are given. Multiple integrals as well as integrals on curves and surfaces are introduced and their interrelations are studied (Green's formula). Applications of these integrals to mechanics and physics are ...

Some classes of ordinary differential equations (ODE) are studied. General and partial solutions of linear ODE in scalar and vector form are constructed. Boundary value problems and eigenstructure problems for linear ODE of second order are considered. Basic facts about curves and surfaces are given. Multiple integrals as well as integrals on curves and surfaces are introduced and their interrelations are studied (Green's formula). Applications of these integrals to mechanics and physics are ...

Some classes of ordinary differential equations (ODE) are studied. General and partial solutions of linear ODE in scalar and vector form are constructed. Boundary value problems and eigenstructure problems for linear ODE of second order are considered. Basic facts about curves and surfaces are given. Multiple integrals as well as integrals on curves and surfaces are introduced and their interrelations are studied (Green's formula). Applications of these integrals to mechanics and physics are ...

Some classes of ordinary differential equations (ODE) are studied. General and partial solutions of linear ODE in scalar and vector form are constructed. Boundary value problems and eigenstructure problems for linear ODE of second order are considered. Basic facts about curves and surfaces are given. Multiple integrals as well as integrals on curves and surfaces are introduced and their interrelations are studied (Green's formula). Applications of these integrals to mechanics and physics are ...

Some classes of ordinary differential equations (ODE) are studied. General and partial solutions of linear ODE in scalar and vector form are constructed. Boundary value problems and eigenstructure problems for linear ODE of second order are considered. Basic facts about curves and surfaces are given. Multiple integrals as well as integrals on curves and surfaces are introduced and their interrelations are studied (Green's formula). Applications of these integrals to mechanics and physics are ...

Some classes of ordinary differential equations (ODE) are studied. General and partial solutions of linear ODE in scalar and vector form are constructed. Boundary value problems and eigenstructure problems for linear ODE of second order are considered. Basic facts about curves and surfaces are given. Multiple integrals as well as integrals on curves and surfaces are introduced and their interrelations are studied (Green's formula). Applications of these integrals to mechanics and physics are ...

The aim of the course is to present the foundations of mathematical methods and their implementation in machine arithmetic. The following issues are considered: elements of floating-point machine arithmetic, properties of computational problems, stability of computational algorithms, estimates of the global error in computational processes, elements of numerical linear algebra and numerical mathematical analysis, mathematical calculations using the program system MATLAB. The above themes are ...

Elements of probability theory are studied: random variable, arithmetic mean, dispersion, co-variation and coefficient of correlation. Basic methods of mathematical statistics are presented - point-wise estimates, maximum like-hood method, test of hypothesis.

Elements of probability theory are studied: random variable, arithmetic mean, dispersion, co-variation and coefficient of correlation. Basic methods of mathematical statistics are presented - point-wise estimates, maximum like-hood method, test of hypothesis.

Elements of probability theory are studied: random variable, arithmetic mean, dispersion, co-variation and coefficient of correlation. Basic methods of mathematical statistics are presented - point-wise estimates, maximum like-hood method, test of hypothesis.

Elements of probability theory are studied: random variable, arithmetic mean, dispersion, co-variation and coefficient of correlation. Basic methods of mathematical statistics are presented - point-wise estimates, maximum like-hood method, test of hypothesis.

Elements of probability theory are studied: random variable, arithmetic mean, dispersion, co-variation and coefficient of correlation. Basic methods of mathematical statistics are presented - point-wise estimates, maximum like-hood method, test of hypothesis.

Elements of probability theory are studied: random variable, arithmetic mean, dispersion, co-variation and coefficient of correlation. Basic methods of mathematical statistics are presented - point-wise estimates, maximum like-hood method, test of hypothesis.

Elements of probability theory are studied: random variable, arithmetic mean, dispersion, co-variation and coefficient of correlation. Basic methods of mathematical statistics are presented - point-wise estimates, maximum like-hood method, test of hypothesis.

Elements of probability theory are studied: random variable, arithmetic mean, dispersion, co-variation and coefficient of correlation. Basic methods of mathematical statistics are presented - point-wise estimates, maximum like-hood method, test of hypothesis.

Facts from the probability theory are given - probability, probability space, random variables. Elements of the theory of transport flows (characteristics, properties) are considered.

1. Determinants, matrixes, systems of linear equations. Vectors – operations and applications. 2. Straight-line and plane equations. Second-order areas. 3. Series. Limit, continuity and derivative of a function – properties and applications. 4. Indefinite and definite integrals – calculation and applications in geometry and physics. 5. Some first-order differential equations. Second-order straight-line differential equations. 6. Oiler’s formula for polyhedrons. Plato bodies.

This course of Mathematics allows students to work with the basic definitions and theorems of Linear Algebra, Analytical Geometry, Analysis of one-argument functions, Differential Equations of order 1, Linear Differential Equations with constant coefficients, partial derivatives of multi-argument functions, applications of integrals.

Elements of Lyapunov stability theory for ordinary differential equations (ODE) are studied: standard, asymptotic and exponential stability, orbital stability, attractors and chaos, stability of linear ODE. Some applications of stability theory to the mechanics of particles and rigid bodies are considered.

Elements of Lyapunov stability theory for ordinary differential equations (ODE) are studied: standard, asymptotic and exponential stability, orbital stability, attractors and chaos, stability of linear ODE. Some applications of stability theory to the mechanics of particles and rigid bodies are considered.

Elements of Lyapunov stability theory for ordinary differential equations (ODE) are studied: standard, asymptotic and exponential stability, orbital stability, attractors and chaos, stability of linear ODE. Some applications of stability theory to the mechanics of particles and rigid bodies are considered.

Elements of Lyapunov stability theory for ordinary differential equations (ODE) are studied: standard, asymptotic and exponential stability, orbital stability, attractors and chaos, stability of linear ODE. Some applications of stability theory to the mechanics of particles and rigid bodies are considered.

Elements of Lyapunov stability theory for ordinary differential equations (ODE) are studied: standard, asymptotic and exponential stability, orbital stability, attractors and chaos, stability of linear ODE. Some applications of stability theory to the mechanics of particles and rigid bodies are considered.

Elements of Lyapunov stability theory for ordinary differential equations (ODE) are studied: standard, asymptotic and exponential stability, orbital stability, attractors and chaos, stability of linear ODE. Some applications of stability theory to the mechanics of particles and rigid bodies are considered.

Elements of Lyapunov stability theory for ordinary differential equations (ODE) are studied: standard, asymptotic and exponential stability, orbital stability, attractors and chaos, stability of linear ODE. Some applications of stability theory to the mechanics of particles and rigid bodies are considered.

Elements of Lyapunov stability theory for ordinary differential equations (ODE) are studied: standard, asymptotic and exponential stability, orbital stability, attractors and chaos, stability of linear ODE. Some applications of stability theory to the mechanics of particles and rigid bodies are considered.

Elements of Lyapunov stability theory for ordinary differential equations (ODE) are studied: standard, asymptotic and exponential stability, orbital stability, attractors and chaos, stability of linear ODE. Some applications of stability theory to the mechanics of particles and rigid bodies are considered.

The course in “Statistics“ includes basic concepts and methods in probability group theory and statistics. The aim of this course is to help the future specialists to learn how to construct efficient schemes for the analyzed systems in the concrete examples and to recognize the accuracy of the exit data. The course includes the basic concepts and theorems in probabilities group theory and statistics – classic probabilities, random variables, the theory of point-wise estimates, correlation ...