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Course detail
FSI-RMAAcad. year: 2023/2024
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
Guarantor
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.
Study aids
Prerequisites and corequisites
Basic literature
Recommended literature
Elearning
Classification of course in study plans
specialization BIO , 1 year of study, winter semester, compulsory-optionalspecialization IME , 1 year of study, winter semester, compulsory
Lecture
Teacher / Lecturer
Syllabus
1. Revision of selected topics2. Metric space, complete metric space3. Contraction, fix-point Banach's theorem and its applications4. Vector space, base, dimension, isomorphism5. Automorphism of vector spaces, eigenvectors and eigenvalues6. Unitary space orthogonal a orthonormal bases7. Hilbert space, L2 and l2 spaces8. Orthogonal bases, Fourier series9. Complex Fourier series, discrete Fourier transform10. Usage of Fourier transform, convolution theorem11. L2 space for functions of more variable12. Operators and functionals in Hilbert space13. Applications
Exercise