Course detail

Mathematics - Fundamentals

FSI-RMBAcad. year: 2024/2025

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

Mode of study

Not applicable.

Guarantor

Mgr. Jana Hoderová, Ph.D.

Department

Institute of Mathematics (ÚM)

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.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Bachman,G., Laerence, N.: Functional analysis, Dover Pub., 1966,2000
Kolmogorov,A.N.,Fomin,S.V.: Elements of the Theory of Functions and Functional Analysis, Graylock Press, 1957, 1961, 2002
Rektorys, K.: Variační metody, Academia Praha, 1999

Recommended reading

Kolmogorov,A.N.,Fomin,S.V.: Základy teorie funkcí a funkcionální analýzy, SNTL Praha 1975
Rektorys, K.: Variační metody, Academia Praha, 1999
Veit, J. Integrální transformace: SNTL, Praha 1979

Classification of course in study plans

  • Programme N-PMO-P Master's 1 year of study, winter semester, compulsory-optional

  • Programme C-AKR-P Lifelong learning

    specialization CZS , 1 year of study, winter semester, elective

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Mgr. Věra Kollárová, Ph.D.

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 hod., compulsory

Teacher / Lecturer

Mgr. Věra Kollárová, Ph.D.

Syllabus

Seminars include practical problems related to the course.