Mathematics II. (E011092)

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

Zkratka: | MA2EN | Schválen: | 24.03.2022 |

Platí do: | ?? | Rozsah: | 4P+4C+0L |

Semestr: | Kredity: | 7 | |

Zakončení: | Z,ZK | Jazyk výuky: | EN |

Anotace

Differential calculus of functions of several variables - domain, graph (quadratic areas)

Continuity, partial derivatives, gradient and its physical meaning, differential, approximate evaluation of function value.

Local extremes, global extremes. Implicit function, its derivative, tangent, resp. tangent plane.

Integral calculus of functions of several variables - Fubini's theorem, calculation of double and triple integrals.

Transformation into polar, cylindrical and spherical coordinates.

Smooth curve, closed curve. Curve integral of scalar and vector functions, Green's theorem.

Smooth surface, closed surface. Area integral of scalar and vector functions. Gauss theorem, Stokes theorem.

Geometric and physical applications of integrals - calculation of surface area and volume of a body, length of a curve.

Weight, center of gravity, moment of inertia.

Work done by force along a curve. Flow of vector field through a surface.

Potential both in E2, and in E3. Independence of the curve integral on the integration path.

Work done by force along a closed curve.

Non-spring vector field. Irrotational field.

Continuity, partial derivatives, gradient and its physical meaning, differential, approximate evaluation of function value.

Local extremes, global extremes. Implicit function, its derivative, tangent, resp. tangent plane.

Integral calculus of functions of several variables - Fubini's theorem, calculation of double and triple integrals.

Transformation into polar, cylindrical and spherical coordinates.

Smooth curve, closed curve. Curve integral of scalar and vector functions, Green's theorem.

Smooth surface, closed surface. Area integral of scalar and vector functions. Gauss theorem, Stokes theorem.

Geometric and physical applications of integrals - calculation of surface area and volume of a body, length of a curve.

Weight, center of gravity, moment of inertia.

Work done by force along a curve. Flow of vector field through a surface.

Potential both in E2, and in E3. Independence of the curve integral on the integration path.

Work done by force along a closed curve.

Non-spring vector field. Irrotational field.

Vyučující

doc. Ing. Tomáš Bodnár Ph.D.

Letní 2023/2024

doc. Ing. Tomáš Bodnár Ph.D.

Letní 2022/2023

Osnova

Differential calculus of functions of several variables - domain, graph (quadratic areas)

Continuity, partial derivatives, gradient and its physical meaning, differential, approximate evaluation of function value.

Local extremes, global extremes. Implicit function, its derivative, tangent, resp. tangent plane.

Integral calculus of functions of several variables - Fubini's theorem, calculation of double and triple integrals.

Transformation into polar, cylindrical and spherical coordinates.

Smooth curve, closed curve. Curve integral of scalar and vector functions, Green's theorem.

Smooth surface, closed surface. Area integral of scalar and vector functions. Gauss theorem, Stokes theorem.

Geometric and physical applications of integrals - calculation of surface area and volume of a body, length of a curve.

Weight, center of gravity, moment of inertia.

Work done by force along a curve. Flow of vector field through a surface.

Potential both in E2, and in E3. Independence of the curve integral on the integration path.

Work done by force along a closed curve.

Non-spring vector field. Irrotational field.

Continuity, partial derivatives, gradient and its physical meaning, differential, approximate evaluation of function value.

Local extremes, global extremes. Implicit function, its derivative, tangent, resp. tangent plane.

Integral calculus of functions of several variables - Fubini's theorem, calculation of double and triple integrals.

Transformation into polar, cylindrical and spherical coordinates.

Smooth curve, closed curve. Curve integral of scalar and vector functions, Green's theorem.

Smooth surface, closed surface. Area integral of scalar and vector functions. Gauss theorem, Stokes theorem.

Geometric and physical applications of integrals - calculation of surface area and volume of a body, length of a curve.

Weight, center of gravity, moment of inertia.

Work done by force along a curve. Flow of vector field through a surface.

Potential both in E2, and in E3. Independence of the curve integral on the integration path.

Work done by force along a closed curve.

Non-spring vector field. Irrotational field.

Literatura

Neustupa J.: Matematics II (skriptum fakulty strojní). Vydavatelství ČVUT, Praha 2008.