Special Functions and Their Symmetries: Postgraduate Course in Applied Analysis
by Vadim Kuznetsov, Vladimir Kisil
Publisher: University of Leeds 2003
This text 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.
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by Simon J.A. Malham - Heriot-Watt University
From the table of contents: Order notation; Perturbation methods; Asymptotic series; Laplace integrals (Laplace's method, Watson's lemma); Method of stationary phase; Method of steepest descents; Bibliography; Notes; Exam formula sheet; etc.
by Guenther Hoermann, Roland Steinbauer - Universitaet Wien
From the table of contents: 1. Test Functions and Distributions; 2. Differentiation, Differential Operators; 3. Basic Constructions; 4. Convolution; 5. Fourier Transform and Temperate Distributions; 6. Regularity; 7. Fundamental Solutions.
by Omran Kouba - arXiv
In these notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications are presented.
by Stanislaw Saks - Polish Mathematical Society
Covering all the standard topics, the author begins with a discussion of the integral in an abstract space, additive classes of sets, measurable functions, and integration of sequences of functions. Succeeding chapters cover Caratheodory measure.