Mathematics - Fundamentals (FSI-RMB)

Academic year 2022/2023
Supervisor: Mgr. Jana Hoderová, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
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 optics. It is designed especially for students who need to improve and deepen their mathematical skills.
Learning outcomes and competences:
Selected chapters of mathematical analysis, Fourier transform, special functions and their application in optics.
Prerequisites:
Mathematical analysis and linear algebra
Course contents:
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.
Teaching methods and criteria:
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.
Controlled participation in lessons:
Missed lessons can be compensated for via a written test.
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Exercise  13 × 2 hrs. compulsory                  
Course curriculum:
    Lecture

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 Seminars include practical problems related to the course.
Literature - fundamental:
1. Kolmogorov,A.N.,Fomin,S.V.: Elements of the Theory of Functions and Functional Analysis, Graylock Press, 1957, 1961, 2002
2. Rektorys, K.: Variační metody, Academia Praha, 1999
3. Bachman,G., Laerence, N.: Functional analysis, Dover Pub., 1966,2000
Literature - recommended:
1. Kolmogorov,A.N.,Fomin,S.V.: Základy teorie funkcí a funkcionální analýzy, SNTL Praha 1975
2. Rektorys, K.: Variační metody, Academia Praha, 1999
3. Veit, J. Integrální transformace: SNTL, Praha 1979
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
CŽV full-time study CZV Bases of Mechanical Engineering -- GCr 5 Compulsory-optional 1 1 W
N-PMO-P full-time study --- no specialisation -- GCr 5 Compulsory-optional 2 1 W