Course detail
Mathematics of Wave Optics
FSI-9MAVAcad. year: 2022/2023
Special functions are frequently used in monographs and papers dealing with wave optics. In spite of that they are not involved in the curricula (e. g. the Lommel functions of two variables or the Fresnel integrals). In some cases a mathematical literature does not exist at all (e. g. the Zernike polynomials). Most of the graduates from the technological universities never studied special functions, not even the standard ones (e. g. the Bessel functions). Therefore, the post-graduate students of optical engineering have troubles with the study of books and papers, with mathematical treatment of their own results, and with numerical calculations. The present course offers an overview of mathematics used in wave optics. The exposition is kept in frames of functions of real variables and applications are emphasized.
Language of instruction
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Applications of special functions in wave optics.
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Sneddon I. N.: Special functions of mathematical physics and chemistry. Oliver and Boyd, Edinburgh 1966. (EN)
Temne N. M.: Special Functions. John Wiley & Sons, Inc., New York 1996. (EN)
Recommended reading
Watson G. N.: A Treatise on the Theory of Bessel Functions. 2nd ed.. Cambridge University Press, Cambridge 1966. (EN)
Whittaker E. T., Watson G. N.: A Course of Modern Analysis. Cambridge University Press, Cambridge 1965. (EN)
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2. Gamma and digamma functions.
3. Sine and cosine integrals.
4. The Fresnel integrals.
5. The Dirac distribution.
6. Orthogonal systems of functions. The Gramm-Schmidt orthogonalization process.
7. Hypergeometric functions.
8. The Bessel functions.
9. The Fourier transform.
10. The Hankel transforms.
11. The Jacobi polynomials.
12. The Gegenbauer polynomials.
13. The Chebyshev polynomials.
14. The Zernike polynomials.