Course detail

Geometrical Algorithms

FSI-0AV Acad. year: 2019/2020 Winter semester

A survey on advanced structures om multi-linear algebra and, consequently, their application in Euclidean space transformation. Introduction to the theory of geometric algebras and algorithms for elementary tasks of analytic geometry. Simple geometric algorithms for the rigid body motion using Euclidean transformations.

Language of instruction

Czech

Number of ECTS credits

3

Learning outcomes of the course unit

Enhancement of skills that are necessary for applying advanced mathematical structures.

Prerequisites

Elementary notions of algebra and linear algebra.

Planned learning activities and teaching methods

The course is taught in lectures explaining the basic principles and theory of the discipline. Calculations in an appropriate software will be presented.

Assesment methods and criteria linked to learning outcomes

Graded assessment: semester project, oral exm.

Aims

Introduction of advanced mathematical structures and their applications in engineering.

Specification of controlled education, way of implementation and compensation for absences

Lectures, non-compulsory attendance.

The study programmes with the given course

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

1. Review: vector space, basis, dimension, scalar product, bilinear and quadratic forms.
2. Euclidean transformations of two and three dimensional space.
3. Symplectic form, volume elements, quadratic spaces.
4. Tensor calculus, Clifford algebra.
5.-6. Introduction to geometric algebras, special cases of CRA (G3,1) and CGA (G4,1).
7.-8. Computation in geometric algebras.
9. Fundamental tasks of analytic geometry in geometric algebras.
10. Software for symbolic calculations and visualisation in geometric algebras (Python, CLUCalc).
11.-12. Euclidean transformations in geometric algebra, rigid body motion.
13. Consultations to semester project.