Course detail

Mathematics - Fundamentals

FSI-RMBAcad. year: 2022/2023

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)

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

Co-requisites

Not applicable.

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.

Course curriculum

Not applicable.

Work placements

Not applicable.

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

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
Bachman,G., Laerence, N.: Functional analysis, Dover Pub., 1966,2000

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 CŽV Lifelong learning

    branch CZV , 1. year of study, winter semester, compulsory-optional

Type of course unit

 

Lecture

26 hours, 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 hours, compulsory

Teacher / Lecturer

Mgr. Věra Kollárová, Ph.D.

Syllabus

Seminars include practical problems related to the course.