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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 Syllabus for a course in dynamical systems (MTTS)
M.Sc. 2 96 downloads so far.
Last downloaded on: 13-02-2019 06:34 AM
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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. 99 downloads so far.
Last downloaded on: 12-02-2019 10:43 AM
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3 Riesz-Fredholm-Schauder Theory Gives a direct proof of Fredhohlm alternative theorem without using spectral theorem for compact operators.
M.Sc. 2 99 downloads so far.
Last downloaded on: 15-02-2019 04:04 AM
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4 Bishop-Stone-Weierstrass Theorem Proves Machado's version of Bishop-Stone-Weierstrass theorem.
2 101 downloads so far.
Last downloaded on: 15-02-2019 04:03 AM
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5 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. 2 101 downloads so far.
Last downloaded on: 14-02-2019 08:16 AM
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6 First Order PDE The Method of Characteristics Explains the geometric ideas underlying the method of charatcteristics
M.Sc. 2 101 downloads so far.
Last downloaded on: 16-02-2019 04:32 PM
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7 One Dimensional Wave Equation One dimensional wave equation via graded exercises
M.Sc. 2 101 downloads so far.
Last downloaded on: 19-02-2019 07:28 AM
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8 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. 2 102 downloads so far.
Last downloaded on: 11-02-2019 01:27 PM
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9 Higher Dimensional Poisson Equation Higher dimensional Poisson/Lapalce equation.
M.Sc. 2 103 downloads so far.
Last downloaded on: 11-02-2019 01:29 PM
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10 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. 2 104 downloads so far.
Last downloaded on: 11-02-2019 05:29 PM
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