Czech

6

Not applicable.

The knowledge and skills obtained during the course will appear on the following fields
1. Passing the course, students will master computing with complex numbers and all forms of their expression including the Euler formulas. They will learn the computation of n-th roots and solving binomial equations.
2. Students manage the classification and solution of the simpliest kinds of first-order differential equations and the n-th order linear differential equations with constant coefficients. They will master its solution by the method of the variation of constants and by the method of improper coefficients. Further, they will be aquainted with
3. Passing the course, students are able follow and apply the methods of differential calculus of n variables. In more details, they learn to find, describe and express domains, graphs, contour lines of functions. They master the concepts of a limit, partial and direction derivative and total differential with their properties. They will be able to find local and global extremes and work with implicitely given functions.
4. Passing the course, students will manage double and triple integrals and their applications.
5. Students will be acquainted with the elements of the field theory, Hamilton operator and fundamental physical fields. They will manage the computation of a potential of a vector field in case it exists.
6. Finishing the course, students will understand the concepts of the curve and surface integral in both of the scalar and vector field in context with the physical meaning. They will be able to decide about the independency of the oriented curve integral on the choice of the oriented integration path and in the positive case compute the integral by means of a potential.
They will be endowed by the knowledge of integral theorems with their physical meaning and applications. They will master the computation of various integrals by the technique of integral theorems.
7. Passing the course, students are expected to solve simple tasks of the physical character appearing in the advanced courses and engineering disciplines. Managing both of the mathematical courses during bachelor studies should enable reading and comprehension the mathematical symbolics used in the literature extending the knowlege in the studied branch.

Differential and integral calculus of functions of one variable, elements of the linear algebra and analytical geometry.
The necessary condition for obtaining credit is having the credit from Mathematics 1 and the examination can be passed only if the examination from Mathematics 1 has been succesfuly passed.

Not applicable.

The course uses teaching methods in form of Lecture - 2 teaching hours per week, seminars - 2 teaching hours per week. The e-learning system (LMS Moodle) is available to teachers and students.

Obtaining a credit is conditioned by a regular and active participation on practices and the credit it is a necessary condition for sitting for an examination. Obtaining credit is conditioned by a successfull passing three tests during the semester and working out the semestral work.The participation on lectures is not obliged. The examination consists of a test ond an oral part. The results from practices are included to the total marking of the subject.

1. Complex numbers - the algebraic, trigonometric and exponential form, binomial equations. Elementary concepts from the theory of ordinary differential equations. MATLAB commands for the work with complex numbers.
2. First-order differential equations, the existence and uniqueness theorem, solution of their simpliest kinds -the separable and homogenous equations.
3. Higher-order linear differential equations with constant coefficients - the method of indefinite coefficients.
4. Higher-order linear differential equations with constant coefficients - the method of the variation of constants .
5. Introductory to the differential calculus of functions of n variables - domains, graphs, contour lines, the concepts of a limit, continuity, partial derivative, total differential, the equation of the tangent hyperplane to the graph. MATLAB graphical commands commands for drawing graphs of functions of two variables and surfaces in general.
6. The concept of total differential, equation of tangent hyperplane to the graph. Local and global extremes of the functions of two variables.
7. The Taylor polynomial, implicitely given functions, the geometrical interpretation.
8. Derivatives of implicitely given functions. Searching local and global for extremes of implicitely given functions.
9. Double and integral - its definition and computation by means of Fubini theorem. Applications. MATLAB commands for the computation of the value of a double integral.
10. The transformation theorem for a double integral. Giving a curve and a surface. MATLAB cgraphical commands for drawing curves and surfaces.
elementary transformations of double and triple integrals. Introductory to the thery of fields, Hamilton operator.
11. The triple integral, its computation bz means of the Fubini theorem, application, elementary transformation of triple integrals.
12. The non-oriented curve integral, applications, the orientation of a curve, the oriented curve integral., applications.
13. Information of the most elementary concepts from the field theory, the independence of the oriented curve integral on the integration path.

Not applicable.

The aim of the course is obtaining the theoretical background necessary for studies of physics, particularly elementary kinds of differential equations, elements of the theory of fields, Hamilton operator and integral theorems.

Necessary conditions for obtaining a credit are the regular participation on practies and reaching at least 50% of marks from tests checking computation skills and the ability of their application to simple problems formulated in words. Moreover, there is a semestral work consisting of 20 computative examples. If a student fails at a test, he has a possibility of its correction.

Not applicable.

Not applicable.

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Eliáš J., Horváth J., Kajan J., Šulka R.: Zbierka úloh z vyššej matematiky. ALFA Bratislava. (CS)
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Smith, R., Minton, R.B.: Calculus - Early Trancscendental Functions. MacGraw Hill, New York. (CS)
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39 hours, compulsory