714-0506/01 – Mathematics IV - IG (M IV)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits4
Subject guarantorRNDr. Jiří Poláček, CSc.Subject version guarantorRNDr. Jiří Poláček, CSc.
Study levelundergraduate or graduateRequirementChoice-compulsory
Year2Semestersummer
Study languageCzech
Year of introduction1999/2000Year of cancellation2004/2005
Intended for the facultiesHGFIntended for study typesMaster
Instruction secured by
LoginNameTuitorTeacher giving lectures
POL12 RNDr. Jiří Poláček, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

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

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 20 (20) 0
                Project Project 6  0
                Written exam Written test 9  0
                Other task type Other task type 5  0
        Examination Examination 80 (80) 0
                Written examination Written examination 60  0
                Oral Oral examination 20  0
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2004/2005 (M3646) Geodézie a kartografie (3646T007) Geodesy Engineering P Czech Ostrava 2 Choice-compulsory study plan
2003/2004 (M3646) Geodézie a kartografie (3646T007) Geodesy Engineering P Czech Ostrava 2 Choice-compulsory study plan
2003/2004 (M3646) Geodézie a kartografie (3646T001) Mine Surveying P Czech Ostrava 2 Choice-compulsory study plan
2002/2003 (M3646) Geodézie a kartografie (3646T007) Geodesy Engineering P Czech Ostrava 2 Choice-compulsory study plan
2002/2003 (M3646) Geodézie a kartografie (3646T001) Mine Surveying P Czech Ostrava 2 Choice-compulsory study plan
2001/2002 (M3646) Geodézie a kartografie (3646T007) Geodesy Engineering P Czech Ostrava 2 Choice-compulsory study plan
2000/2001 (M3646) Geodézie a kartografie (3646T001) Mine Surveying P Czech Ostrava 2 Choice-compulsory study plan
2000/2001 (M3646) Geodézie a kartografie (3646T007) Geodesy Engineering P Czech Ostrava 2 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner