Academic year 2023/2024 |
Supervisor: | doc. Mgr. Petr Vašík, Ph.D. | |||
Supervising institute: | ÚM | |||
Teaching language: | Czech | |||
Course type: | departmental course, applied basis | |||
Aims of the course unit: | ||||
The course aims to acquaint the students with the basics of algebraic operations, linear algebra, vector and Euclidean spaces, and analytic geometry. This will enable them to attend further mathematical and engineering courses and deal with engineering problems. Another goal of the course is to develop the students' logical thinking. |
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Learning outcomes and competences: | ||||
Students will be made familiar with algebraic operations,linear algebra, vector and Euclidean spaces, and analytic geometry. They will be able to work with matrix operations, solve systems of linear equations and apply the methods of linear algebra to analytic geometry and engineering tasks. When completing the course, the students will be prepared for further study of mathematical and technical disciplines. | ||||
Prerequisites: | ||||
Students are expected to have basic knowledge of secondary school mathematics. | ||||
Course contents: | ||||
The course deals with the following topics: Vector spaces, matrices and operations on matrices. Consequently, determinants, matrices in a step form and the rank of a matrix, systems of linear equations. Euclidean spaces: scalar product of vectors, eigenvalues and eigenvectors, Jordan canonical form. Fundamentals of analytic geometry, linear objects. |
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Teaching methods and criteria: | ||||
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures. | ||||
Assesment methods and criteria linked to learning outcomes: | ||||
Course-unit credit requirements: Active attendance at the seminars, at least 50% of points in written tests. There is one alternative date to correct these tests. Form of examinations: The exam is written and has two parts. The exercises part takes 100 minutes and 6 exercises are given to solve. The theoretical part takes 20 minutes and 6 questions are asked. At least 50% of the correct results must be obtained from each part. If less is met in one of the parts, then the classification is F (failed). Exercises are evaluated by 3 points, questions by 1 point. If 50% of each part is met, the total classification is given by the sum. A (excellent): 22 - 24 points B (very good): 20 - 21 points C (good): 17 - 19 points D (satisfactory): 15 - 16 points E (enough): 12 - 14 points F (failed): 0 - 11 points |
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Controlled participation in lessons: | ||||
Attendance at lectures is recommended, attendance at seminars is required. The lessons are planned on the basis of a weekly schedule. The way of compensation for an absence is in the competence of the teacher. | ||||
Type of course unit: | ||||
Lecture | 13 × 3 hrs. | optionally | ||
Exercise | 11 × 2 hrs. | compulsory | ||
Computer-assisted exercise | 2 × 2 hrs. | compulsory | ||
Course curriculum: | ||||
Lecture | 1. Number sets, fields. Vector spaces, subspaces, homomorphisms. |
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Exercise | Week 1: Fundamental notions such as vectors, matrices and operations. |
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Computer-assisted exercise | Seminars with computer support are organized according to current needs. They enables students to solve algorithmizable problems by computer algebra systems. |
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Literature - fundamental: | ||||
1. Slovák J., Lineární algebra, Masarykova univerzita, http://www.math.muni.cz/~slovak/ftp/lectures/linearni.algebra/ |
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2. Thomas, G. B., Finney, R.L.: Calculus and Analytic Geometry, Addison Wesley 2003. | ||||
3. Howard, A. A.: Elementary Linear Algebra, Wiley 2002. | ||||
4. Rektorys, K. a spol.: Přehled užité matematiky I., II., Prometheus 1995. | ||||
5. Searle, S. R.: Matrix Algebra Useful for Statistics, Wiley 1982. | ||||
Literature - recommended: | ||||
6. Karásek, J., Skula, L.: Algebra a geometrie, Cerm 2002. | ||||
7. Nedoma, J.: Matematika I., Cerm 2001. | ||||
8. Nedoma, J.: Matematika I., část první: Algebra a geometrie, PC-DIR 1998. | ||||
9. Horák, P., Janyška, J.: Analytická geometrie, Masarykova univerzita 1997. | ||||
10. Janyška, J., Sekaninová, A.: Analytická teorie kuželoseček a kvadrik, Masarykova univerzita 1996. | ||||
11. Mezník, I., Karásek, J., Miklíček, J.: Matematika I. pro strojní fakulty, SNTL 1992. | ||||
12. Horák, P.: Algebra a teoretická aritmetika, Masarykova univerzita 1991. | ||||
13. Procházka, L. a spol.: Algebra, Academia 1990. |
The study programmes with the given course: | |||||||||
Programme | Study form | Branch | Spec. | Final classification | Course-unit credits | Obligation | Level | Year | Semester |
B-MAI-P | full-time study | --- no specialisation | -- | Cr,Ex | 6 | Compulsory | 1 | 1 | W |
MITAI | full-time study | NEMB do 2021/22 Embedded Systems | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
MITAI | full-time study | NSPE Sound, Speech and Natural Language Processing | -- | Cr,Ex | 6 | Compulsory | 1 | 0 | W |
MITAI | full-time study | NBIO Bioinformatics and Biocomputing | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
MITAI | full-time study | NSEN Software Engineering | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
MITAI | full-time study | NVIZ Computer Vision | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
MITAI | full-time study | NGRI Computer Graphics and Interaction | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
MITAI | full-time study | NADE Application Development | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
MITAI | full-time study | NISD Information Systems and Databases | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
MITAI | full-time study | NMAT Mathematical Methods | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
MITAI | full-time study | NSEC Cybersecurity | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
MITAI | full-time study | NISY do 2020/21 Intelligent Systems | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
MITAI | full-time study | NCPS Cyberphysical Systems | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
MITAI | full-time study | NHPC High Performance Computing | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
MITAI | full-time study | NNET Computer Networks | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
MITAI | full-time study | NMAL Machine Learning | -- | Cr,Ex | 6 | Compulsory | 1 | 0 | W |
MITAI | full-time study | NVER Software Verification and Testing | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
MITAI | full-time study | NIDE Intelligent Devices | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
MITAI | full-time study | NEMB Embedded Systems | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
MITAI | full-time study | NISY Intelligent Systems | -- | Cr,Ex | 6 | Elective | 1 | 0 | W |
Faculty of Mechanical Engineering
Brno University of Technology
Technická 2896/2
616 69 Brno
Czech Republic
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