CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2022/2023
UPOZORNĚNÍ: Jsou dostupné studijní plány pro následující akademický rok.

# Mathematics II.

Code Completion Credits Range Language
E011092 Z,ZK 7 4P+4C+0L English
Garant předmětu:
Tomáš Bodnár
Lecturer:
Tomáš Bodnár, Hynek Řezníček
Tutor:
Tomáš Bodnár, Hynek Řezníček
Supervisor:
Department of Technical Mathematics
Synopsis:

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.

Requirements:
Syllabus of lectures:

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.

Syllabus of tutorials:
Study Objective:
Study materials:

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

Note:
Time-table for winter semester 2022/2023:
Time-table is not available yet
Time-table for summer semester 2022/2023:
 06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00 roomKN:A-313Bodnár T.10:45–12:15(lecture parallel1)Karlovo nám.Učebna KA313 roomKN:A-313Řezníček H.09:00–10:30(lecture parallel1parallel nr.101)Karlovo nám.Učebna KA313 roomKN:A-313Bodnár T.09:00–10:30(lecture parallel1)Karlovo nám.Učebna KA313 roomKN:A-313Řezníček H.09:00–10:30(lecture parallel1parallel nr.101)Karlovo nám.Učebna KA313
The course is a part of the following study plans:
Data valid to 2023-06-01
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet7157206.html