Course detail
Mathematics - Selected Topics
FSI-RMAAcad. year: 2024/2025
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
Number of ECTS credits
Mode of study
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.
Study aids
Prerequisites and corequisites
Basic literature
Kolmogorov,A.N.,Fomin,S.V.: Elements of the Theory of Functions and Functional Analysis, Graylock Press, 1957, 1961, 2002
Rektorys, K.: Variační metody, Academia Praha, 1999
Recommended reading
Rektorys, K.: Variační metody, Academia Praha, 1999
Veit, J. Integrální transformace: SNTL, Praha 1979
Elearning
Classification of course in study plans
- Programme N-IMB-P Master's
specialization BIO , 1 year of study, winter semester, compulsory-optional
specialization IME , 1 year of study, winter semester, compulsory - Programme N-MET-P Master's 1 year of study, winter semester, compulsory
- Programme N-PMO-P Master's 1 year of study, winter semester, compulsory-optional
- Programme C-AKR-P Lifelong learning
specialization CZS , 1 year of study, winter semester, elective
Type of course unit
Lecture
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
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
Elearning