Czech

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.

Not applicable.

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

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.
2. First-order differential equations, solution of their simpliest kinds, i.e. separable and linear equations.
3. Higher-order linear differential equations with constant coefficients - the method of the variation of constants and the method of indefinite coefficients.
4. 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.
5. Local and global extremes, the Taylor polynomial.
6. Implicitely given functions, the geometrical interpretation. Searching for extremes of implicitely given functions.
7. Double and triple integrals, their definition and computation by means of Fubini theorem. Applications.
8. The transformation theorem, elementary transformations of double and triple integrals. Introductory to the thery of fields, Hamilton operator.
9. Elementary kinds of physical fields, the computation of a potential. Curves and their basic kinds, the orientation of a curve.
10. The oriented and the non-oriented curve integrals, their physical meaning and applications. The indipendence of an oriented curve integral on the choice of an oriented path.
11. The concept of a surface and its orientation, the oriented and the non-oriented surface integral.
12. Physical and geometrical applications of both kinds of the surface integral. Stokes and Green theorem.
13. Gauss-Ostrogradski theorem, the physical meaning if the integral theorems.

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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