Course detail
Mathematics - Fundamentals
FSI-RMB Acad. year: 2023/2024 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
Entry knowledge
Mathematical analysis and linear algebra
Rules for evaluation and completion of the course
Course-unit credit and exam are based on a written test.
Missed lessons can be compensated for 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 optics. It is designed especially for students who need to improve and deepen their mathematical skills.
Selected chapters of mathematical analysis, Fourier transform, special functions and their application in optics.
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. Derivative of a fuction.
5. Partial derivative of a functions, differential operators.
6. Indefinite and definite integral.
7. Double integral, physical applications.
8. 2D Fourier transform and its application
9. Taylor and Maclaurin series.
10. Elementary functions. Special functions used in optics.
11. Special functions used in optics.
12. Filtration in space and frequency domain, applications in optics.
Exercise
26 hours, compulsory
Teacher / Lecturer
Syllabus
Seminars include practical problems related to the course.