Special Functions and Their Symmetries \ Postgraduate Course in Applied Analysis

# Special Functions and Their Symmetries Postgraduate Course in Applied Analysis

University of Leeds, School of Mathematics

 Lecturers: Vadim Kuznetsov (Room 9.18h) and Vladimir Kisil (Room 8.18l) Web page: http://maths.leeds.ac.uk/~kisilv/courses/special.html

Description: This course is suitable for postgraduate students in both applied and pure mathematics. It presents fundamentals of special functions theory and its applications in partial differential equations of mathematical physics. The course covers topics in harmonic, classical and functional analysis, and combinatorics. It consists of the two parts: the first part gives the classic analytical approach and the second links the theory with groups of symmetries. The main objective of the course is to learn how:

• to determine types of PDEs which may be solved by application of special functions.

• to analyze properties of special functions by their integral representations and symmetries.

• to classify differential equations by their singularities; to obtain properties of solutions of PDE by their symmetries.

To print lecture notes use PostScript files of the first and the second parts. See Technical notes on viewing online materials.
Contents:

Pre-requisites: Basic real and complex analysis, rudimentary algebra.

## References

[1]
George E. Andrews, Richard Askey, and Ranjan Roy. Special functions. Cambridge University Press, Cambridge, 1999.

[2]
Willard Miller, Jr. Lie Theory and Special Functions. Academic Press, New York, 1968. Mathematics in Science and Engineering, Vol. 43.

[3]
N. Ja. Vilenkin. Special Functions and the Theory of Group Representations. American Mathematical Society, Providence, R. I., 1968. Translated from the Russian by V. N. Singh. Translations of Mathematical Monographs, Vol. 22.
Tecnical Notes:
• If you experienced a problem reading the course HTML pages then an easy solution could be found in Help on Browser Problems or (even better) use the PDF files (see bellow).

• PDF version is provided online and preferable in many respects. Acrobat Reader for your computer platform could be obtained free of charge.