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Course info
KMA / GS1
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Course description
Department/Unit / Abbreviation
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KMA
/
GS1
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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 1
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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,
4
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
2
[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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|
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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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237 / -
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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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0 / -
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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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Summer semester
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Semester taught
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Summer 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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The course provides fundamental conditions for bachelor technical study fields. Students are able to use mathematical methods (linear algebra, analytic geometry) and methods of projection to the plane (Monge projection and axonomery). The course also aims at giving the student a firm understanding of analytic method in the visualization of mathematical concepts, it develops the student's skills to solve problems using the combined sythetic and analytic method and finally it shows several applications not only in mathematical disciplines but mainly in technical or natural sciences.
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Requirements on student
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*Confirmation of fulfillment of course requirements*
It is stipulated by the course guarantor that the credits earned for the prevevious successful fulfillment of course requirements are not accepted.
Condition for fulfillment of course requirements is at least 21 points (15 points from each of two tests and 10 points from assigments during semester).
In case the student does not reach 21 points, an extra test is given reflecting topics from two original tests.
*Bonus to exam*
Students who achieve outstanding results (more than 30 points from 40) gain a special bonus, in particular 31 and 32 points means +1 point to the exam, 33 and 34 points means +2 points to the exam, etc.
*Examination*
The exam consists of A) a written, and B) an oral part.
Written part
- Time is 90'
- On can obtain up to 10 points for each example from the test.
- The written part consists of 4 problems oriented on:
- matrices, determinants, eigenvalues and eigen vectors, inverse matrix
- solvability of systems of linear equations, homogeneous equations, geometric interpretation
- elementary surfaces and related problems(intersections, tangent planes) in axonometry
- fundumental problems solved by the analytical methods
Oral part
- The oral examination is focused on the analysis of the written part and on related topics (10 points).
- Two further theoretical topics reflecting the lecture topics are given.
- To pass the exam the student is obliged to gain at leat 2 points from the oral exam otherwise he/she fails no matter what the result of the written part is.
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Content
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1. Polynomials.
2. Matriices. Detereminants.
3. Systems of linear equations and their solvability.
4. Inverse matrix. Eigenvalues and eigenvectors.
5. Ideal elements. Introduction to methods of projection.
6. Axonometry.
7. Orthogonal axonometry. Afinity and collineation.
8. Elementary surfaces
9. Vector algebra 1
10. Vector algebra 2 - scalar, vector and triple product/multiplication.
11. Analytic geometry 1 - mutual positions
12. Analytic geometry 1 - metric problems
13. Summary
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Activities
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Link to: CourseWare:
KMA/GS1
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Link to Google Classroom: :
Rozvrhová akce KMA/GS1 (2023/24, LS) - Čt 07:30-09:10, UC-236
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Link to Google Classroom: :
Rozvrhová akce KMA/GS1 (2023/24, LS) - Čt 09:20-11:00, UC-236
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Link to Google Classroom: :
Rozvrhová akce KMA/GS1 (2023/24, LS) - So 12:05-14:40, UC-210, Týden: 7
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Link to Google Classroom: :
Rozvrhová akce KMA/GS1 (2023/24, LS) - Út 09:20-11:00, EU-308
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Link to Google Classroom: :
Rozvrhová akce KMA/GS1 (2023/24, LS) - Út 14:50-16:30, UC-210
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Fields of study
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Guarantors and lecturers
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Guarantors:
Doc. Ing. Bohumír Bastl, Ph.D. ,
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Lecturer:
Doc. Ing. Bohumír Bastl, Ph.D. (100%),
Doc. RNDr. Michal Bizzarri, Ph.D. (100%),
RNDr. Světlana Tomiczková, Ph.D. (100%),
Mgr. Radek Výrut (100%),
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Tutorial lecturer:
Doc. Ing. Bohumír Bastl, Ph.D. (100%),
Doc. RNDr. Michal Bizzarri, Ph.D. (100%),
Ing. Kristýna Slabá, Ph.D. (100%),
Mgr. Zuzana Štauberová (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 1. Pomocný učební text
(Ježek, František - Míková, Marta - Tomiczková, Světlana)
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Extending:
Deskriptivní geometrie
(Tomiczková, Světlana)
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Extending:
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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Recommended:
Štauberová, Zuzana. Mongeovo promítání. 1. vyd. V Plzni : Západočeská univerzita, 2004. ISBN 80-7043-323-X.
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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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Individual project (40)
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10
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Preparation for an examination (30-60)
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45
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Preparation for formative assessments (2-20)
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20
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Contact hours
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52
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Total
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127
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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: |
have an understanding of basic concepts of elementary geometry and trigonometry in the extent of high school curriculum |
have an understanding of basic principles of projection methods and know fundamentals of at least one projection method, preferably Monge's projection |
have an understanding of basic principles of elementary calculus |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
apply acquired skills of basic geometric problems at high school level |
apply techniques of suitable projection method (preferably Monge's projection) on basic problems |
apply methods of calculus on basic problems |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
have an understanding of concepts and methods in linear algebra (matrices, determinants, vector spaces, solving of systems of linear equations) |
have an understanding of concepts and methods in analytic geometry, especially in 3D (position and metric problems) |
have an understanding of concepts and methods in descriptive geometry, especially Monge's projection and axonometry) |
be knowledgeable in description of basic geometric objects, especially selected special classes of surfaces |
Skills - skills resulting from the course: |
decompose complex geometric problems to a sequence of elementary constructions |
apply methods of linear algebra (matrices, determinants, vector spaces, solving of systems of linear equations) on solving of suitable problems |
actively use analytic method in solving fundamental and applied problems |
use techniques and methods of Monge's projection and axonometry |
analyse selected geometric properties, especially with respect to their use in student's subject of study and future professional expertise |
find and use application potential not only in geometry, but also in technical and natural sciences, industrial design, CAD, etc. |
Competences - competences resulting from the course: |
N/A |
N/A |
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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 |
Test |
Skills - skills achieved by taking this course are verified by the following means: |
Combined exam |
Test |
Competences - competence achieved by taking this course are verified by the following means: |
Combined exam |
Test |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Practicum |
Task-based study method |
Individual study |
Skills - the following training methods are used to achieve the required skills: |
Lecture |
Practicum |
Task-based study method |
Individual study |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Practicum |
Task-based study method |
Individual study |
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