Course detail
Mathematics - Fundamentals
FSI-RMB Acad. year: 2021/2022 Winter semester
The course familiarises students with selected topics of mathematics which are necessary for study of optics and related subjects. The main attention is paid to mathematical analysis, work with functions and applications in optics.
Language of instruction
Czech
Number of ECTS credits
5
Supervisor
Department
Learning outcomes of the course unit
Selected chapters of mathematical analysis, Fourier transform, special functions and their application in optics.
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 and exam are based on 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 optics. It is designed especially for students who need to improve and deepen their mathematical skills.
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 N-PMO-P: Precise Mechanics and Optics, Master's, compulsory-optional
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
1. Vector space, base, dimension.
2. Complex number, Gaussian plane, complex functions.
3. Basics of the matrix algebra.
4. Derivation of 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
Seminars include practical problems related to the course.