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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 Higher Dimensional Poisson Equation Higher dimensional Poisson/Lapalce equation.
M.Sc. 2 51 downloads so far.
Last downloaded on: 11-06-2018 09:25 PM
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2 Proofs of Malgrange-Ehrenpreis Theorem Aims to give different proofs of local solvability of PDO's with constant coefficient. INCOMPLETE
Ph.D. 52 downloads so far.
Last downloaded on: 19-06-2018 12:22 PM
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3 Gives a proof as graded exercises. As an application, Tietze extension theorem for $\R^n$ is proved.
M.Sc. 2 53 downloads so far.
Last downloaded on: 15-06-2018 11:40 AM
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4 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 54 downloads so far.
Last downloaded on: 13-06-2018 02:11 PM
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5 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 54 downloads so far.
Last downloaded on: 15-06-2018 11:39 AM
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6 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 54 downloads so far.
Last downloaded on: 18-06-2018 09:13 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. 55 downloads so far.
Last downloaded on: 19-06-2018 11:59 PM
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8 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 55 downloads so far.
Last downloaded on: 19-06-2018 12:25 PM
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9 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 55 downloads so far.
Last downloaded on: 18-06-2018 10:50 AM
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10 Gives a complete straightforward proof of Tyknoff's theorem about the compactness of arbitrary products of compact spaces.
M.Sc. 2 55 downloads so far.
Last downloaded on: 15-06-2018 11:41 AM
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