714-0506/01 – Mathematics IV - IG (M IV)
Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 4 |
Subject guarantor | RNDr. Jiří Poláček, CSc. | Subject version guarantor | RNDr. Jiří Poláček, CSc. |
Study level | undergraduate or graduate | Requirement | Choice-compulsory |
Year | 2 | Semester | summer |
| | Study language | Czech |
Year of introduction | 1999/2000 | Year of cancellation | 2004/2005 |
Intended for the faculties | HGF | Intended for study types | Master |
Subject aims expressed by acquired skills and competences
This course is closed.
Teaching methods
Summary
Vectors and matrices: linear representation, the matrices of linear
representation, the transmission matrix and coordinate transformation, matrices
of the composite and inverse representations. Spherical trigonometry: basic
terms, the law of sines, the law of cosines for the sides and the angles, half-
side and angle formulas, Gauss formulas, the rectangular spherical triangle,
Neper rule, the solution of a spherical triangle. Differential geometry of
curves and surfaces: the vector function of a scalar argument, plane and space
curves, the Frenet trihedron, the 1st and the 2nd curvature, the 1st and the
2nd basic form of the plane. Asymptotic directions, the principal directions of
a surface, the principal, Gaussian, medium and geodesic curvatures of a
surface. The three-dimensional integral: definition, Fubini’s theorem,
transformation into cylindrical and spherical coordinates, applications.
Compulsory literature:
Škrášek, J – Tichý, Z.: Základy aplikované matematiky II. SNTL, Praha 1986,
Demlová, M. – Nagy, J.: Algebra. MVŠT. SNTL, Praha 1985,
Budinský, B. Analytická a diferenciální geometrie. MVŠT. SNTL, Praha 1983.
Recommended literature:
Way of continuous check of knowledge in the course of semester
E-learning
Other requirements
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.