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.
In case of any problem with downloading, please write to mttsonlineservices+exparticles@gmail.com.
Sl No  Title  Description  Targeted Audience  MTTS Level  Downloads 
1  Existence and Uniqueness of Solutions of ODE Smooth Flow Associated to a Smooth Vectorfield  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  66 downloads so far. Last downloaded on: 13082018 05:47 PM Download now 
2  Higher Dimensional Poisson Equation  Higher dimensional Poisson/Lapalce equation. 
M.Sc.  2  66 downloads so far. Last downloaded on: 13082018 05:47 PM Download now 
3  Gives a proof as graded exercises. As an application, Tietze extension theorem for $\R^n$ is proved. 
M.Sc.  2  66 downloads so far. Last downloaded on: 13082018 05:48 PM Download now 

4  Any compact hypersurface in R n is a level surface (1) Orientability of Hypersurfaces in R n (2) JordanBrouwer Separation Theorem  In this note, we prove JordanBrouwer 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  67 downloads so far. Last downloaded on: 13082018 05:47 PM Download now 
5  Higher Dimensional Wave Equation  Outline of the results on wave equations of higher dimensions, closely following McOwen's book (Sections 3.2 and 3.3) 
M.Sc.  2  67 downloads so far. Last downloaded on: 13082018 05:47 PM Download now 
6  Geometric Applications of Sturm Comparison Theorem  After recalling the Sturm's comparison theorem, we
illustrate some of its typical applications in the theory of
surfaces. Even though some acquaintance with Gauss theory of
surfaces will be advantageous, it is not absolutely
necessary, as I have striven to illustrate the uses in the case
of a sphere in 3space. 
M.Sc./Ph.D  2  67 downloads so far. Last downloaded on: 13082018 05:47 PM Download now 
7  Gives a complete straightforward proof of Tyknoff's theorem about the compactness of arbitrary products of compact spaces. 
M.Sc.  2  67 downloads so far. Last downloaded on: 13082018 05:47 PM Download now 

8  BishopStoneWeierstrass Theorem  Proves Machado's version of BishopStoneWeierstrass theorem. 
2  68 downloads so far. Last downloaded on: 13082018 05:46 PM Download now 

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  68 downloads so far. Last downloaded on: 13082018 05:47 PM Download now 
10  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  68 downloads so far. Last downloaded on: 13082018 05:47 PM Download now 
Page 1 of 21 Total Results 202
*****************************************************************