Czech

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Institute of Mathematics and Descriptive Geometry (MAT)

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.

The students should be versed in the basic notions of the theory of functions of one and several variables (derivative, partial derivative, limit, continuous functions, graphs of functions). They should be able to calculate integrals of function of one variable, know their basic applications.

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Requirements for successful completion of the subject are specified by guarantor’s regulation updated for every academic year.

1. Definition of double integral, basic properties and calculation.
2. Transformations and applications of double integral.
3. Definition of triple integral, basic properties and calculation.
4. Transformations and applications of triple integral.
5. Notion of a curve. Curvilinear integral in a scalar field and its applications.
6. Vector field. Divergence and rotation of a vector field. Curvilinear integral in a vector field and its applications.
7. Green`s theorem and its application.
8. Independence of a curvilinear integral on the integration path.
9. Basics of ordinary differential equations.
10. First order differential equations - separable, linear, exact equations.
11. N-th order homogeneous linear differential equations with constant coefficients.
12. Solutions to non-homogeneous linear differential equations.
13. Variation-of-constants method.

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Students should learn the basics about double and tripple integrals and their applications, they should know how to calculate such integrals using the Fubini theorems and standard transformations, get familiar with line integrals both in a scalar and vector field and their applications, calculate simple line integrals.
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.

Extent and forms are specified by guarantor’s regulation updated for every academic year.

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BUDINSKÝ, Bruno a CHARVÁT, Jura: Matematika II. SNTL, Praha, 1990. ISBN 80-03-00219-2. (CS)
DANĚČEK, Josef, DLOUHÝ, Oldřich a PŘIBYL, Oto: Dvojný a trojný integrál. CERM Brno, 2006. ISBN 80-7204-453-2. (CS)
DANĚČEK, Josef, DLOUHÝ, Oldřich a PŘIBYL, Oto: Křivkové integrály. CERM Brno, 2006. ISBN 80-7204-452-4. (CS)
DIBLÍK, Josef a PŘIBYL,Oto: Obyčejné diferenciální rovnice. CERM Brno, 2004. ISBN 80-214-2795-7. (CS)
REKTORYS, Karel a spol.: Přehled užité matematiky I. Prometheus, Praha, 1995. (CS)
ŠKRÁŠEK, Josef a TICHÝ, Zdeněk: Základy aplikované matematiky II. SNTL Praha, 1986. ISBN 04-513-86. (CS)

HŘEBÍČKOVÁ, Jana, SLABĚŇÁKOVÁ, Jana a ŠAFÁŘOVÁ, Hana: Sbírka příkladů z matematiky II. Stavební fakulta VUT Brno, CERM, 2008. ISBN 978-80-7204-606-5. (CS)
KOUTKOVÁ, Helena a PRUDILOVÁ, Květoslava: Sbírka příkladů z matematiky III. Stavební fakulta VUT Brno, CERM, 2008. ISBN 978-80-7204-598-3. (CS)
LANG, Serge: Calculus of several variables. New York: Springer Verlag, 1988. (EN)
STEIN, Sherman. K.: Calculus and analytic geometry. New York: McGraw-Hill, 1989. (EN)