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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 Bishop-Stone-Weierstrass Theorem Proves Machado's version of Bishop-Stone-Weierstrass theorem.
2 103 downloads so far.
Last downloaded on: 27-03-2019 09:02 AM
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2 Syllabus for a course in dynamical systems (MTTS)
M.Sc. 2 103 downloads so far.
Last downloaded on: 17-04-2019 07:54 AM
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3 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. 2 105 downloads so far.
Last downloaded on: 12-04-2019 12:18 PM
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4 Riesz-Fredholm-Schauder Theory Gives a direct proof of Fredhohlm alternative theorem without using spectral theorem for compact operators.
M.Sc. 2 105 downloads so far.
Last downloaded on: 27-03-2019 11:01 PM
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5 pi_ 1 (S n ) is trivial for n greater than or equal to 2 Proves that the fundamental group of $S^n$ is trivial for $n\geq 2$. A rigorous geometric proof. Of course, there are simpler proofs which use a little sophisticated machinery.
M.Sc. 2 105 downloads so far.
Last downloaded on: 25-03-2019 12:58 AM
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6 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. 107 downloads so far.
Last downloaded on: 15-04-2019 04:01 AM
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7 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. 2 109 downloads so far.
Last downloaded on: 26-03-2019 09:40 PM
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8 Weyl’s Integral and Character Formulas for U (n) Weyl integral and character formula for $U(n)$. Includes Braching law for $U(n)$. This was a handout to a 700 level course at Indiana University, Bloomington during the year 1983-84. There is complete set of handouts for the 2 semester course. I plan to type all of them as and when I find time.
Ph.D. 109 downloads so far.
Last downloaded on: 09-04-2019 05:29 PM
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9 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. 2 110 downloads so far.
Last downloaded on: 30-03-2019 02:29 PM
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10 First Order PDE — The Method of Characteristics Explains the geometric ideas underlying the method of charatcteristics
M.Sc. 2 110 downloads so far.
Last downloaded on: 12-04-2019 09:50 PM
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