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Course detail
Mathematics - selected topics
| Subjet code : | FSI-RMA |
|---|---|
| Faculty: | Faculty of Mechanical Engineering |
| Academic year: | 2011/2012 |
| Open: | Yes |
| Supervisor: | prof. RNDr. Miloslav Druckmüller, CSc. |
| Department: | Institute of Mathematics |
| Study level: | Master's |
| Study form: | full-time study |
| Language of instruction: | Czech |
| Number of credits: | 5 |
| Completion: | graded course-unit credit |
| Year of study: | 1 |
| Semester: | winter |
| Duty: | compulsory |
The study programmes with the given course
Objective of the course – aims of the course unit: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. | |
Objective of the course – learning outcomes and competences: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 | |
Course contents (annotation):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. | |
Teaching methods and criteria:Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations. | |
Assesment methods and criteria linked to learning outcomes:Course-unit credit - based on a written test | |
Specification of controlled education, way of implementation and compensation for absences:Missed lessons can be compensated for via a written test. | |
Recommended reading:Kolmogorov,A.N.,Fomin,S.V.: Elements of the Theory of Functions and Functional Analysis, Graylock Press, 1957, 1961, 2002 |
Type of course unit:
| Lecture: | 26 hours, optionally |
|---|---|
| Teacher: | prof. RNDr. Miloslav Druckmüller, CSc. |
| 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 |
| seminars: | 26 hours, compulsory |
| Teacher: | prof. RNDr. Miloslav Druckmüller, CSc. |
| 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 |
