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
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
Missed lessons can be compensated for via a written test.
Aims
Selected chapters of mathematical analysis, Fourier transform, special functions and their application in optics.
Study aids
Prerequisites and corequisites
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
Recommended reading
Rektorys, K.: Variační metody, Academia Praha, 1999
Veit, J. Integrální transformace: SNTL, Praha 1979
Classification of course in study plans
Type of course unit
Lecture
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
Teacher / Lecturer
Syllabus