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Download MTTS Expository Articles

The articles are prepared by Prof. S Kumaresan, the MTTS Programme Director and usually gets distributed to the MTTS/ Mini MTTS/ PTMT participants.

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Sl No Title Description Targeted Audience MTTS Level Downloads
1 Syllabus for a course in dynamical systems (MTTS)
M.Sc. 2 91 downloads so far.
Last downloaded on: 15-12-2018 07:06 PM
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2 Plancherel Theorem and Fourier Inversion Theorem An experiment which succeeded. It is traditional to prove the Fourier inversion first and then derive Planceral theorem. Here we reverse the order and thereby learn a few tricks of analysis.
M.Sc. 2 95 downloads so far.
Last downloaded on: 15-12-2018 07:06 PM
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3 Local Solvability of Constant Coefficient Differential Operators It establishes the local solvability of constant coefficient partial differential operator using Hormander's a priori inequality.
Ph.D. 95 downloads so far.
Last downloaded on: 15-12-2018 07:03 PM
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4 Geometric Applications of Sturm Comparison Theorem After recalling the Sturm's comparison theorem, we illustrate some of its typical applications in the theory of surfaces. Even though some acquaintance with Gauss theory of surfaces will be advantageous, it is not absolutely necessary, as I have striven to illustrate the uses in the case of a sphere in 3-space.
M.Sc./Ph.D 2 95 downloads so far.
Last downloaded on: 15-12-2018 07:07 PM
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5 Gives a complete straightforward proof of Tyknoff's theorem about the compactness of arbitrary products of compact spaces.
M.Sc. 2 95 downloads so far.
Last downloaded on: 15-12-2018 07:08 PM
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6 Gives an accessible proof of the regularity of solutions of elliptic equations. Needs careful proof-reading
annoyingly trivail math erros! Ph.D. 96 downloads so far.
Last downloaded on: 15-12-2018 07:09 PM
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7 Any compact hypersurface in R n is a level surface (1) Orientability of Hypersurfaces in R n (2) Jordan-Brouwer Separation Theorem In this note, we prove Jordan-Brouwer Separation theorem and the orientability of hypersurface in $\R^n$. In fact, both are easy consequences of the main result which says that any compact hypersurface is a level set of a smooth function defined on all of $\R^n$.
M.Sc./Ph.D 2 96 downloads so far.
Last downloaded on: 15-12-2018 07:06 PM
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8 Existence and Uniqueness of Solutions of ODE Smooth Flow Associated to a Smooth Vector-field Local existence, uniqueness and smooth flow associated with a ODE; for a slighly more matured audience; may be found in my book on DG and Lie groups.
M.Sc. 2 96 downloads so far.
Last downloaded on: 15-12-2018 07:07 PM
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9 First Order PDE The Method of Characteristics Explains the geometric ideas underlying the method of charatcteristics
M.Sc. 2 96 downloads so far.
Last downloaded on: 15-12-2018 07:07 PM
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10 Higher Dimensional Poisson Equation Higher dimensional Poisson/Lapalce equation.
M.Sc. 2 97 downloads so far.
Last downloaded on: 15-12-2018 07:07 PM
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