Lectures on Topics in Analysis
by Raghavan Narasimhan
Publisher: Tata Institute of Fundamental Research 1965
Number of pages: 205
Topics covered: Differentiable functions in Rn; Manifolds; Vector bundles; Linear differential operators; Cauchy Kovalevski Theorem; Fourier transforms, Plancherel's theorem; Sobolev spaces Hm,p; Elliptic differential operators; etc.
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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 Victor Guillemin, Shlomo Sternberg - Harvard University
In semi-classical analysis many of the basic results involve asymptotic expansions in which the terms can by computed by symbolic techniques and the focus of these lecture notes will be the 'symbol calculus' that this creates.
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.
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.