by I.M. Sigal, M. Merkli
Publisher: University of Toronto 2001
Number of pages: 176
In this course, we deal with modern analysis. Properties of functions are studied as much as they are needed for understanding maps. More specifically, our emphasis is on applications of modern analysis and the material is selected accordingly.
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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.
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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.
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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.
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Contents: Infinite Dimensional Vector Spaces; Fourier Theory; Sturm-Liouville Theory; Green's Function Theory; Special Function Theory; Partial Differential Equations; System of Partial Differential Equations: How to Solve Maxwell's Equations ...