Course detail
Mathematics - Selected Topics
FSI-RMA Acad. year: 2023/2024 Winter semester
The course familiarises studetns with selected topics of mathematics which are necessary for study of mechanics, mechatronics 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
Entry knowledge
Mathematical analysis and linear algebra in the extent of the first two years of study.
Rules for evaluation and completion of the course
Classified course-unit credit based on a written test
Missed lessons can be compensated via a written test.
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.
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.
The study programmes with the given course
Programme N-MET-P: Mechatronics, Master's, compulsory
Programme N-PMO-P: Precise Mechanics and Optics, Master's, compulsory-optional
Programme N-IMB-P: Engineering Mechanics and Biomechanics, Master's
specialization BIO: Biomechanics, compulsory-optional
Programme N-IMB-P: Engineering Mechanics and Biomechanics, Master's
specialization IME: Engineering Mechanics, compulsory
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
1. Revision of selected topics
2. Metric space, complete metric space
3. Contraction, fix-point Banach's theorem and its applications
4. Vector space, base, dimension, isomorphism
5. Automorphism of vector spaces, eigenvectors and eigenvalues
6. Unitary space orthogonal a orthonormal bases
7. Hilbert space, L2 and l2 spaces
8. Orthogonal bases, Fourier series
9. Complex Fourier series, discrete Fourier transform
10. Usage of Fourier transform, convolution theorem
11. L2 space for functions of more variable
12. Operators and functionals in Hilbert space
13. Applications
Exercise
26 hours, compulsory
Teacher / Lecturer
Syllabus
1. Revision of selected topics
2. Metric space, complete metric space
3. Contraction, fix-point Banach's theorem and its applications
4. Vector space, base, dimension, isomorphism
5. Automorphism of vector spaces, eigenvectors and eigenvalues
6. Unitary space orthogonal a orthonormal bases
7. Hilbert space, L2 and l2 spaces
8. Orthogonal bases, Fourier series
9. Complex Fourier series, discrete Fourier transform
10. Usage of Fourier transform, convolution theorem
11. L2 space for functions of more variable
12. Operators and functionals in Hilbert space
13. Applications