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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 Proofs of Malgrange-Ehrenpreis Theorem Aims to give different proofs of local solvability of PDO's with constant coefficient. INCOMPLETE
Ph.D. 25 downloads so far.
Last downloaded on: 22-04-2018 03:59 AM
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2 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 27 downloads so far.
Last downloaded on: 19-04-2018 10:05 AM
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3 Syllabus for a course in dynamical systems (MTTS)
M.Sc. 2 27 downloads so far.
Last downloaded on: 20-04-2018 10:34 AM
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4 Gives an accessible proof of the regularity of solutions of elliptic equations. Needs careful proof-reading
annoyingly trivail math erros! Ph.D. 27 downloads so far.
Last downloaded on: 20-04-2018 10:41 AM
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5 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 28 downloads so far.
Last downloaded on: 13-03-2018 01:17 PM
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6 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 28 downloads so far.
Last downloaded on: 20-04-2018 10:46 AM
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7 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. 28 downloads so far.
Last downloaded on: 23-04-2018 01:33 AM
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8 Gives a proof as graded exercises. As an application, Tietze extension theorem for $\R^n$ is proved.
M.Sc. 2 28 downloads so far.
Last downloaded on: 20-04-2018 11:11 AM
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9 Frobenius theorem on the classification real associative division algebras are $\R$, $\C$ and the quaternions. Accessible to students who have learnt linear algebra.
Final year B.Sc, M.Sc 1,2 29 downloads so far.
Last downloaded on: 22-04-2018 03:31 AM
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10 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 29 downloads so far.
Last downloaded on: 20-04-2018 06:32 PM
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