Course detail
Mathematics - Fundamentals
FSI-RMB Acad. year: 2020/2021 Winter semester
The course familiarises studetns with selected topics of mathematics which are necessary for study of mechanics and related subjects. It deals with spaces of functions, orthogonal systems of functions, orthogonal transformations and numerical methods used in mechanics.
Language of instruction
Czech
Number of ECTS credits
5
Supervisor
Department
Learning outcomes of the course unit
Basic knowledge of functional analysis, metric, vector, unitary spaces, Hilbert space, orthogonal systems of functions, orthogonal transforms, Fourier transform and spectral analysis, application of mentioned subjects in mechanics and physics.
Prerequisites
Mathematical analysis and linear algebra
Planned learning activities and teaching methods
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 – based on a written test
Exam has a written and (possibly) and oral part.
Aims
The aim of the course is to extend students´knowledge acquired in the basic mathematical courses by the topics necessary for study of mechanics and related subjects.
Specification of controlled education, way of implementation and compensation for absences
Missed lessons can be compensated for via a written test.
The study programmes with the given course
Programme M2A-P: Applied Sciences in Engineering, Master's
branch M-PMO: Precise Mechanics and Optics, compulsory-optional
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
1. Mapping, binary relations, equivalence, factor set
2. Metric space
3. Contraction, fix point Banach's theorem
4. Vector space, base, dimension, Vector spaces of functions
5. Unitary space orthogonal a orthonormal spaces
6. Hilbert space, L2 and l2 space
7. Orthogonal bases, Fourier series
8. Orthogonal transforms, Fourier transform, spectral analysis
9. Usage of Fourier transform, convolution theorem, filters
10. 2D Fourier transform and its application
11. Filtration in space and frequency domain, applications in physics and mechanics
12. Operators and functionals
13. Variation methods
Exercise
26 hours, compulsory
Teacher / Lecturer
Syllabus
1. Revision of selected topics
2. Metric space
3. Contraction, fix point Banach's theorem
4. Vector space, base, dimension, Vector spaces of functions
5. Unitary space orthogonal a orthonormal spaces
6. Hilbert space, L2 and l2 space
7. Orthogonal bases, Fourier series
8. Orthogonal transforms, Fourier transform, spectral analysis
9. Usage of Fourier transform, convolution theorem, filters
10. 2D Fourier transform and its application
11. Filtration in space and frequency domain, applications in physics and mechanics
12. Operators and functionals
13. Variation methods