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Mathematics II. A (E01A068)

Departments: | ústav technické matematiky (12101) | ||

Abbreviation: | Approved: | 21.04.2017 | |

Valid until: | ?? | Range: | 0P+0C |

Semestr: | Credits: | 3 | |

Completion: | ZK | Language: | EN |

Annotation

Open and closed set, boundary in E^k. Real function of k-variables. Partial derivatives and differentiability. Gradient and directional derivative. Differential operators div (divergence) and curl (rotation). Function given implicitly. Local and global (= absolute) extremes of a function of more

variables.

Double integral, volume (=triple) integral,

Fubini theorem. Transformation of integrals to polar, cylindrical and spherical coordinates. A simple smooth curve and line integral of a scalar and vector function.

Circulation and Green's theorem.

A potential vector field, independence of a line integral on the path. Simple smooth surface and surface integral of a scalar function and a vector function. Flow of a vector field through a surface. The Gauss-Ostrogradskij theorem.

variables.

Double integral, volume (=triple) integral,

Fubini theorem. Transformation of integrals to polar, cylindrical and spherical coordinates. A simple smooth curve and line integral of a scalar and vector function.

Circulation and Green's theorem.

A potential vector field, independence of a line integral on the path. Simple smooth surface and surface integral of a scalar function and a vector function. Flow of a vector field through a surface. The Gauss-Ostrogradskij theorem.

Structure

Literarture

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