Course detail

# Mathematics 3

FAST-BA003Acad. year: 2023/2024

Double and triple integrals. Their calculation, transformation, physical and geometric interpretation.

Curvilinear integral in a scalar field, its calculation and application. Divergence and rotation of a vector field. Curvilinear integral in a vector field, its calculation and application. Independence of a curvilinear integral on the integration path. Green`s theorem.

Existence and uniqueness of solutions to first order differential equations. n-th order homogeneous linear differential equations with constant coefficients. Solutions to non-homogeneous linear differential equations with special-type right-hand sides. Variation-of-constants method.

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They should learn the basic facts on selected first-order differential equations, on existence and uniqueness of solutions, be able to find analytical solutions to separated, linear, 1st-order homogeneous, and exact differential equations, calculate the solution of a non-homogeneous linear nth-order differential equation with special right-hand sides as well as using the general method of the variation of constants, understand the structure of solutions to non-homogeneous nth-order linear differential equations.

Knowledge of double and triple integrals, their calculation and application. Knowledge of curvilinear integral in a scalar and vector field, their calculation and application. Knowledge of basic facts on existence, uniqueness and analytical methods of solutions on selected first-order differential equations and nth-order linear differential equations.

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Prerequisites and corequisites

Basic literature

Jirásek, F., Čipera, S., Vacek, M., Sbírka řešených příkladů z matematiky II, SNTL Praha 1986.

(CS)Eliáš, J., Horváth, J., Kajan, J., Śulka, R., Zbierka úloh z vzššej matamatiky 3 a 4, Alfa Bratislava 1979.

(SK)Recommended reading

Škrášek, J., Tichý Z., Základy aplikované matematiky II, Praha SNTL 1986.

(CS)Classification of course in study plans

- Programme B-P-C-SI (N) Bachelor's
branch VS , 2. year of study, winter semester, compulsory

- Programme B-K-C-SI (N) Bachelor's
branch VS , 2. year of study, winter semester, compulsory

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