Advanced Calculus and Analysis
by Ian Craw
Publisher: University of Aberdeen 2000
Number of pages: 110
An introductory Calculus course, with some leanings to analysis, at one time given in second year. It covers sequences, monotone convergence, limits and continuity, differentiability, infinite series, power series, differentiation of functions of several variables, and multiple integrals.
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by Vadim Kuznetsov, Vladimir Kisil - University of Leeds
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.
by Sean Mauch - Caltech
Advanced mathematical methods for scientists and engineers, it contains material on calculus, functions of a complex variable, ordinary differential equations, partial differential equations and the calculus of variations.
by E. E. Rosinger - arXiv
These notes offer a short and rigorous introduction to Nostandard Analysis, mainly aimed to reach to a presentation of the basics of Loeb integration, and in particular, Loeb measures. The Abraham Robinson version of Nostandard Analysis is pursued.
by Raghavan Narasimhan - Tata Institute of Fundamental Research
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.