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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 First Order PDE The Method of Characteristics Explains the geometric ideas underlying the method of charatcteristics
M.Sc. 2 80 downloads so far.
Last downloaded on: 10-10-2018 12:33 PM
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2 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. 80 downloads so far.
Last downloaded on: 19-10-2018 12:52 PM
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3 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 81 downloads so far.
Last downloaded on: 19-10-2018 12:53 PM
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4 Syllabus for a course in dynamical systems (MTTS)
M.Sc. 2 82 downloads so far.
Last downloaded on: 19-10-2018 12:53 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 82 downloads so far.
Last downloaded on: 19-10-2018 12:53 PM
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6 Approximate Identities Starting with a definition of an approximate identity, it gives examples of Fejer's kernel, Landau's kernel, Poisson kernel and Weierstrass kernel and their uses. A must read to master one of the basic tricks in harmonic analysis.
M.Sc. 2 84 downloads so far.
Last downloaded on: 13-10-2018 06:44 AM
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7 Gives an accessible proof of the regularity of solutions of elliptic equations. Needs careful proof-reading
annoyingly trivail math erros! Ph.D. 84 downloads so far.
Last downloaded on: 19-10-2018 12:54 PM
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8 Vector Fields on Spheres a la Milnor A sketch (mainly steps) of the original proof due to Milnor of Hairy ball theorem.
M.Sc. 2 84 downloads so far.
Last downloaded on: 10-10-2018 12:32 PM
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9 Maximum Principle Heat Equation Seems to be a subset of pde8_heat.pdf
84 downloads so far.
Last downloaded on: 19-10-2018 12:54 PM
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10 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 84 downloads so far.
Last downloaded on: 19-10-2018 12:54 PM
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