230-0441/01 – Descriptive Geometry (DG)

Gurantor department	Department of Mathematics	Credits	5
Subject guarantor	Mgr. Dagmar Dlouhá, Ph.D.	Subject version guarantor	Mgr. Dagmar Dlouhá, Ph.D.
Study level	undergraduate or graduate	Requirement	Compulsory
Year	2	Semester	summer
		Study language	Czech
Year of introduction	2019/2020	Year of cancellation
Intended for the faculties	HGF	Intended for study types	Bachelor

Instruction secured by
Login	Name	Tuitor	Teacher giving lectures
DLO44	Mgr. Dagmar Dlouhá, Ph.D.
VOL18	RNDr. Jana Volná, Ph.D.

Extent of instruction for forms of study
Form of study	Way of compl.	Extent
Full-time	Credit and Examination	2+2

Subject aims expressed by acquired skills and competences

• to train development of space abilities • to handle by different types of projection methods, to understand to their principles, to be familiar with their properties, advantages and disadvantages • to acquaint with geometric characteristics of curves and surfaces that are used in technical practice of a given specialization

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

Summary

Descriptive geometry is a practical discipline which tries to improve development of space and creative abalities and logical thinking. First it shows commonly used types of projection methods. At the socond part the geometric characteristics of relevant curves and surfaces folows.

Compulsory literature:

Vavříková,E.:Descriptive Geometry,VŠB – TU,Ostrava 2005, ISBN 80-248-1006-9. http://mdg.vsb.cz/portal/dg/DeskriptivniGeometrie.pdf Černý, J.: Geometry. Praha: Vydavatelství ČVUT, 1996. ISBN 80-01-01535-1. Stillwell, J.: Geometry of surfaces. New York: Springer, 1992. ISBN 0-387-97743-0.

Recommended literature:

Kreyszig, E.: Differential geometry. New York: Dover Publications, 1991. ISBN 0-486-66721-9. Kobayashi, S.: Transformation groups in differential geometry. Berlin: Springer, 1972. Classics in mathematics. ISBN 3-540-05848-6. Umehara, M. and Yamada, K.: Differential geometry of curves and surfaces. Kaiteiban. Translate Rossman, W.. Singapore: World Scientific, 2017. ISBN 978-981-4740-23-4. Falconer, K. J. Fractal geometry: mathematical foundations and applications. 3rd ed. Chichester: Wiley, 2014. ISBN 978-1-119-94239-9.

Way of continuous check of knowledge in the course of semester

Conditions for obtaining the course-unit credit: participation in exercises, 30% of absences can be excused, submission of programs assigned by the supervisor in the prescribed course. The student will get 0-20 b for fulfilling the conditions. (The student who gets the credit will be evaluated 5 - 20 b). The condition for participation in the exam is a written credit from the relevant course. The exam consists of a written and an oral part. Students must pass both parts of the exam and achieve the necessary number of points.

E-learning

Other requirements

Other requirements for students are placed.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Improper elements. Conics - basic concepts and focal properties. 2. Construction of ellipse, hyperbola and parabola from given elements. 3. The basic properties of projection. Parallel projection. 4. Central collineations and axial affinity in plane. 5. Projection with dimensions - view of point, line and plane. 6. Projection with dimensions - position tasks. 7. Projection with dimensions - metric problems. 8. Affine relationship between circle and ellipse. Projection of a circle in the projection with dimensions. 9. Orthogonal axonometry. Position tasks. 10. Metric problems and the projection of a circle in coordinate planes. 11. Elementary surfaces and solids. Basic concepts and properties. 12. Planar cut. Intersections with a line. Tangent plane. 13. Topographical surfaces. 14. Reserve.

Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)

Task name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
Credit and Examination	Credit and Examination	100 (100)	51
Credit	Credit	20	5
Examination	Examination	80 (80)	30	3
Písemná zkouška	Written examination	60	25
Ústní zkouška	Oral examination	20	5

Mandatory attendence participation: At least 70% attendance at the exercises. Absence, up to a maximum of 30%, must be excused and the apology must be accepted by the teacher (the teacher decides to recognize the reason for the excuse).

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Conditions for subject completion and attendance at the exercises within ISP: Mandatory participation in the course is not required. Other conditions for subject completion will respect the individual needs of the student.

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Occurrence in study plans

Academic year	Programme	Branch/spec.	Form	Study language	Tut. centre	Year	Type of duty
2024/2025	(B0532A330040) Applied Geology		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B0724A290001) Mining of Mineral Resources		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B0724A290004) Petroleum Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B0724A290006) Process Engineering in Raw Materials		P	Czech	Ostrava	1	Compulsory	study plan
2023/2024	(B0532A330040) Applied Geology		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0724A290001) Mining of Mineral Resources		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0724A290004) Petroleum Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0724A290006) Process Engineering in Raw Materials		P	Czech	Ostrava	1	Compulsory	study plan
2023/2024	(B3646) Geodesy and Cartography	(3646R007) Engineering Geodesy	P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0724A290001) Mining of Mineral Resources		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0724A290004) Petroleum Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0724A290006) Process Engineering in Raw Materials		P	Czech	Ostrava	1	Compulsory	study plan
2022/2023	(B0532A330040) Applied Geology		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B1316) Geodesy, Cartography and Geoinformatics	(3646R006) Geoinformatics	P	Czech	Ostrava	2	Choice-compulsory	study plan
2022/2023	(B3646) Geodesy and Cartography	(3646R001) Mining Surveying	P	Czech	Most	2	Compulsory	study plan
2022/2023	(B3646) Geodesy and Cartography	(3646R001) Mining Surveying	P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B3646) Geodesy and Cartography	(3646R007) Engineering Geodesy	P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B0724A290004) Petroleum Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B0724A290001) Mining of Mineral Resources		P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B0724A290006) Process Engineering in Raw Materials		P	Czech	Ostrava	1	Compulsory	study plan
2021/2022	(B3646) Geodesy and Cartography	(3646R001) Mining Surveying	P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B3646) Geodesy and Cartography	(3646R007) Engineering Geodesy	P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B1316) Geodesy, Cartography and Geoinformatics	(3646R006) Geoinformatics	P	Czech	Ostrava	2	Choice-compulsory	study plan
2020/2021	(B0724A290001) Mining of Mineral Resources		P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B3646) Geodesy and Cartography	(3646R007) Engineering Geodesy	P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B3646) Geodesy and Cartography	(3646R007) Engineering Geodesy	P	Czech	Most	2	Compulsory	study plan
2020/2021	(B1316) Geodesy, Cartography and Geoinformatics	(3646R006) Geoinformatics	P	Czech	Ostrava	2	Choice-compulsory	study plan
2020/2021	(B3646) Geodesy and Cartography	(3646R001) Mining Surveying	P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B0724A290006) Process Engineering in Raw Materials		P	Czech	Ostrava	1	Compulsory	study plan
2020/2021	(B0724A290004) Petroleum Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(B3646) Geodesy and Cartography	(3646R001) Mining Surveying	P	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(B2111) Mining	(2101R014) Blasting Operations in Mining Engineering	P	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(B1316) Geodesy, Cartography and Geoinformatics	(3646R006) Geoinformatics	P	Czech	Ostrava	2	Choice-compulsory	study plan
2019/2020	(B0724A290001) Mining of Mineral Resources		P	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(B2111) Mining	(2101R013) Mining of Mineral Resources and Their Utilization	P	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(B3646) Geodesy and Cartography	(3646R007) Engineering Geodesy	P	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(B3646) Geodesy and Cartography	(3646R007) Engineering Geodesy	P	Czech	Most	2	Compulsory	study plan
2019/2020	(B2102) Mineral Raw Materials	(2102R013) Processing of Raw Materials and Recycling	P	Czech	Ostrava	2	Compulsory	study plan

Occurrence in special blocks

Block name	Academic year	Form of study	Study language	Year	W	S	Type of block	Block owner

Assessment of instruction