Course: Geometry for mechanical engineering 2

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Course title Geometry for mechanical engineering 2
Course code KMA/GS2
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study not specified
Semester Winter and summer
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Bizzarri Michal, RNDr. Ph.D.
  • Ježek František, Doc. RNDr. CSc.
  • Výrut Radek, Mgr.
  • Tomiczková Světlana, RNDr. Ph.D.
  • Vršek Jan, RNDr. Ph.D.
Course content
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

Learning activities and teaching methods
Individual study, Lecture, Practicum
  • Contact hours - 39 hours per semester
  • Individual project (40) - 20 hours per semester
  • Preparation for an examination (30-60) - 40 hours per semester
prerequisite
professional knowledge
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).
learning outcomes
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.
teaching methods
Lecture
Practicum
Individual study
assessment methods
Combined exam
Recommended literature
  • Budinský, B. Analytická a diferenciální geometrie. 1. vyd. Praha : SNTL, 1983.
  • Ježek, František; Míková, Marta. Maticová algebra a analytická geometrie. 2., přeprac. vyd. Plzeň : Západočeská univerzita, 2003. ISBN 80-7082-996-6.
  • Štauberová, Zuzana. Axonometrie, křivky, plochy. 1. vyd. V Plzni : Západočeská univerzita, 2004. ISBN 80-7043-322-1.
  • Urban, Alois. Deskriptivní geometrie. II.. Praha : SNTL, 1979.
  • Urban, Alois. Deskriptivní geometrie. I.. Praha : SNTL, 1977.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Mechanical Engineering - Materials Engineering and Engineering Metallurgy (1) Mechanical engineering and mechanical production 2 Winter
Faculty of Mechanical Engineering - Industrial Engineering and Management (1) Mechanical engineering and mechanical production 2 Winter
Faculty of Mechanical Engineering - Design of Manufacturing Machines and Equipment (1) Mechanical engineering and mechanical production 2 Winter
Faculty of Mechanical Engineering - Design of Power Machines and Equipment (1) Mechanical engineering and mechanical production 2 Winter
Faculty of Mechanical Engineering Road Vehicles Diagnostics and Service (1) Mechanical engineering and mechanical production 2 Winter
Faculty of Mechanical Engineering - Design of Power Machines and Equipment (1) Mechanical engineering and mechanical production 2 Winter
Faculty of Mechanical Engineering Transport Vehicles and Handling Machinery (1) Mechanical engineering and mechanical production 2 Winter
Faculty of Mechanical Engineering - Materials Engineering and Engineering Metallurgy (1) Mechanical engineering and mechanical production 2 Winter
Faculty of Mechanical Engineering Transport Vehicles and Handling Machinery (1) Mechanical engineering and mechanical production 2 Winter
Faculty of Mechanical Engineering Manufacturing Processes - Technology of Metal Cutting (1) Mechanical engineering and mechanical production 2 Winter
Faculty of Mechanical Engineering - Industrial Engineering and Management (1) Mechanical engineering and mechanical production 2 Winter
Faculty of Mechanical Engineering Manufacturing Processes - Technology of Metal Cutting (1) Mechanical engineering and mechanical production 2 Winter
Faculty of Mechanical Engineering - Design of Manufacturing Machines and Equipment (1) Mechanical engineering and mechanical production 2 Winter