Vudohn Differential equations and their applications. To familiarize students with eliptic curves and the basic notions of the analytic geometry in space. This course consists of 45 hours of lectures and 45 hours of exercises. The analytic geometry in space, vectors in space, scalar product, vector product and mixed product, equations of lines and planes, the relative position of lines and planes. Jurlewicz, Z.

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Find the parallel and perpendicular components of a vector relative to another vector. State the definition of orthogonal trans- formation and describe properties of orthogonal matrices. Definicje, twierdzenia, wzory; [5] Mostowski A. Derivatives of higher order.

The greatest common divisor. Some basic information about the module Use Sylvester criterion to determine positive- and negative-definiteness of quadratic forms. The positive evaluation of the two colloquia is a prerequisite for admission to the test. Two one-hour exams at class times and a final exam. Matrices and systems of linear equations. The main aim of study: Solving of any systems kiniowa linear equations using Cramer theorem and Kronecker-Cappeli theorem. Determine and compute the oriented measures: Lecture, 15 hours more information Tutorials, 30 hours more information.

Production Engineering and Management. In special cases, the assessment may be increased by half a degree. Describe the transformation of the matrix of a linear operator under a change of basis. Student has a knowledge of mathematics including algebra, analysis, functions of one and multiple variables, analytical geometry. Additional information registration calendar, class conductors, localization and schedules of classesmight be available in the USOSweb system: Give the conditions for the matrix of an operator to be diagonalizable.

The goal of the skoczylqs and classes is to achieve knowledge in the area of basic mathematics in order to have a better understanding of the theory of other subjects, core subjects as well as specialized subjects in which mathematical methods are used. Mathematics — part-time first-cycle studies Mathematics — full-time first-cycle studies Additional information registration calendar, class conductors, localization and schedules of classesmight be available in the USOSweb system: Use eigenvalues and eigenvectors to perform diagonalization of a real symmetric matrix.

Lines, planes, hyperplanes in Rn. Explain the geometrical meaning of transformations that shift a conic into canonical form. Zadaania of activities on real numbers and algebraic expressions. The faculty Electrical and Computer Engineering. Integration by parts and by substitution. Rank of a matrix, determinant of a square matrix. Be able to reduce an equation of second-degree curve in R2 into canonical form.

The name of the module department: Convert between polar and Cartesian coordinates. Lecture, 15 hours more information Tutorials, 15 hours more information. You are not logged in log in. Basic mathematical knowledge of secondary school. Basic requirements in category knowledge: Operations on complex numbers. The final grade is the grade of exam, it can be gone up an extra exam in jurpewicz case if the grade of classes is higher.

State the definitions and the geometric meaning of the dot and cross product direction perpendicular to two vectors, oriented area of a parallelogram. Functins and their properties.

This course is related to the following study programmes:. Observe that almost all notions of Euclidean affine geometry can be generalized to higher dimensions in a natural way. The name of the faculty organization unit: After completing this course, student should be able to: Given parametric or normal equations establish the relative position between lines, planes and points. Exponential, logarithmic and inverse-trygonometrical functions. Derive and formulate in terms of the cross product Cramer?

Mathematics 1 Additional information registration calendar, class conductors, localization and schedules of classesmight be available in the USOSweb system:. The skofzylas details of the coordinator: Linear algebra Objectives of the course: Explain the relation between the oriented volume and the generalized cross product of a system of n-1 vectors.

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