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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 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. 19 downloads so far.
Last downloaded on: 24-11-2017 02:30 PM
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2 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 20 downloads so far.
Last downloaded on: 24-11-2017 02:22 PM
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3 Proofs of Malgrange-Ehrenpreis Theorem Aims to give different proofs of local solvability of PDO's with constant coefficient. INCOMPLETE
Ph.D. 20 downloads so far.
Last downloaded on: 24-11-2017 02:29 PM
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4 Sturmís Separation and Comparison Theorems Sturm's separation and oscillation theorems.
M.Sc. 2 22 downloads so far.
Last downloaded on: 24-11-2017 02:21 PM
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5 Starts with Milnor's proof of Hairy-ball theorem, adapts his argument to prove non-retraction theorem, proves Brouwer fixed point theorem. Ends up with a proof of non-retraction using Stokes theorem.
M.Sc. 2 23 downloads so far.
Last downloaded on: 26-12-2017 09:55 AM
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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. 23 downloads so far.
Last downloaded on: 24-11-2017 02:17 PM
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7 Jordan Curve Theorem The aim of this article is to prove that if $\Gamma$ is a subset of $\R^2$ that is homeomorphic to $S^1$, then $\R^2\setminus \Gamma$ has two connected components. The proof uses some basic results in homotopy theory and covering spaces. It has a strong analytic flavour.
M.Sc./Ph.D 2 23 downloads so far.
Last downloaded on: 26-12-2017 10:14 AM
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8 Starting with the definition of harmonic functions and their properties, it gives a solution of Dirichlet problem using Perron;s method of subharmonic functions. It ends up with a discussion of the boundary behaviour. A must read for those who like hard-analysis.
M.Sc./Ph.D 2 24 downloads so far.
Last downloaded on: 24-11-2017 02:14 PM
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9 Frenet-Serre Formulas for Space Curves This article to introduce the readers to a modern outlook of Serre-Frenet Formulas via the Maurer-Cartan forms. While the treatment is hetrogeneous, a diligent reader can cull an elementary introduction as well as a more advanced perspective of these formulas.
M.Sc. 2 24 downloads so far.
Last downloaded on: 24-11-2017 02:14 PM
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10 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 25 downloads so far.
Last downloaded on: 30-11-2017 10:37 PM
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