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Course info
KMA / GS2
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Course description
Department/Unit / Abbreviation
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KMA
/
GS2
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Geometry for mechanical engineering 2
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
3
Cred.
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Type of completion
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-
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Type of completion
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-
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Time requirements
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Lecture
2
[Hours/Week]
Tutorial
1
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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106 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Winter semester
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Semester taught
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Winter semester
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Minimum (B + C) students
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1
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
Yes
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Fundamental course |
No
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Fundamental theoretical course |
Yes
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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N/A
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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This subject is focused on geometry of curves and surfaces in close connection to mechanical engineering, namely to mechanics, processing, design, robotics and CAD/CAM application.
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Requirements on student
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Conditions for obtaining credit is to solve tree excercises during seminars:
- Transformation,
- Rotation and screw surfaces (tangential properties, normal, cuts, common curves),
- Envelope surface (characteristic, cut).
The exam consists of written and oral part. Students have the available table on the types of quadratic objects.
Time for processing of the three examples is 90 minutes. Examples are thematically focused as follows:
1) Transformation - expression in matrix form, determinant, inverse transformation, presentation of the situation in axonometry.
2) Curves -- Interpolation - Lagrange polynomial, spline functions. Approximation - method of least squares. .
3) Surfaces - rotational and screw, quadratic surfaces; projection (tangent plane, normal, cuts) and calculating (equation, tangent plane, normal).
4) Technical surfaces - developable and envelope surfaces, projection and equation.
The oral examination deals with the analysis of written and conceptual apparatus (test) and the general context of reciting the substance. The test is included in the decision on the type specific kvadriky.
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Content
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1. Transformations (coordinates and objects) in E2 and E3
2. Differential geometry of curves - matematical reprezentation, tangent vector, curvature
3. Curves - plane curves, helix
4. Differential geometry of surfaces - matematical reprezentation, tangent plane, curvatures (Gauss curvature)
5.Interpolation - Lagrange polynomial, spline functions. Approximation - method of least squares.
6. Surfaces - classification, problems for surfaces
7. Rotational and helix surfaces - equation, meridian, tangent plane, cuts, common curve
8. Envelope surfaces - characteristic, equation, methods of tanget sphere and plane.
9. Developable surface - classification, development
10. Quadrics - equation, signature, classification, split of common curve
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Activities
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Fields of study
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Guarantors and lecturers
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-
Guarantors:
RNDr. Světlana Tomiczková, Ph.D. (100%),
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Lecturer:
RNDr. Světlana Tomiczková, Ph.D. (100%),
Mgr. Radek Výrut (100%),
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Tutorial lecturer:
Doc. Ing. Bohumír Bastl, Ph.D. (100%),
RNDr. Světlana Tomiczková, Ph.D. (100%),
Doc. RNDr. Jan Vršek, Ph.D. (100%),
Mgr. Radek Výrut (100%),
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Literature
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Basic:
Geometrie pro FST 2
(Ježek, František - Tomiczková, Světlana)
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Recommended:
Budinský, B. Analytická a diferenciální geometrie. 1. vyd. Praha : SNTL, 1983.
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Recommended:
Štauberová, Zuzana. Axonometrie, křivky, plochy. 1. vyd. V Plzni : Západočeská univerzita, 2004. ISBN 80-7043-322-1.
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Recommended:
Urban, Alois. Deskriptivní geometrie. I.. Praha : SNTL, 1977.
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Recommended:
Urban, Alois. Deskriptivní geometrie. II.. Praha : SNTL, 1979.
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Recommended:
Ježek, František; Míková, Marta. Maticová algebra a analytická geometrie. 2., přeprac. vyd. Plzeň : Západočeská univerzita, 2003. ISBN 80-7082-996-6.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Contact hours
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39
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Preparation for an examination (30-60)
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40
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Individual project (40)
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20
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Total
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99
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
General prerequisity is basic knowledge in differential calculus (one and more variables), linear algebra, analytical geometry, and projection methods (content is given by subjects MS1, MS2, and GS1). |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
Student is able to describe curves and surfaces which are used in mechanical engineering and he/she is able to construct orthogonal projection of this objects and to solve geometric problems on surfaces (tangets, curvatures, cuts, common curve, development). Student uses graphics and computational methods. |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Practicum |
Individual study |
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