TEW Differential Equations, Mathematical Modelling and Analysis (2018)

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Venue: Deshbandhu College,  Delhi, Delhi
Date:  24th, Jul 2018 to 29th, Jul 2018

 

School Convener(s)

Name Prof. Abhay Bhatt Ms. Harindri Chaudhary
Mailing Address

Indian Statistical Institute Delhi

Associate Professor Department of Mathematics
Deshbandhu College
Kalkaji , New Delhi - 110019.ur

 


 Speakers with their affiliations:

Name of the speaker

Position

Affiliation

V.D. Sharma Professor IIT Bombay
Inder K. Rana Professor IIT Bombay
Tanvi Jain Professor ISI Dehli
Mani Mehra Professor IIT Delhi
Mukund Madhav Mishra Professor Hansraj College, University of Delhi

 


Syllabus:

Name of the Speaker with affiliation No. of Lectures Detailed Syllabus
Prof. V.D. Sharma
IIT Bombay
9 Method of characteristics and general solution of first order PDEs;
Riemann problem; conservation laws and Burger’s equations;
Cauchy problem for second order PDEs.
First order ordinary differential equations, growth and decay model.
Euler’s equation. Power series solution of a differential equation
about an ordinary point, solution about a regular singular point.
Prof. Inder K. Rana
IIT Bombay
6 From Rationals to reals, understanding limits, from Riemann integration
to Lebesgue integration.
Dr. Tanvi Jain
ISI, Delhi
5

Metric spaces - examples, sequences, continuity, complete and compact metric spaces.
Introduction to convex functions and Fixed point theory.

 

Prof. Mani Mehra
IIT, Delhi
3 Classification of second order PDEs. Complete study of one
dimensional parabolic equation.
Dr. Mukund Madhav Mishra
Hansraj College,
University of Delhi
1 Fourier Series and its convergence.

Details:

Prof. I. K. Rana from IIT Bombay started his lecture with emphasis on the historical importance of Real Analysis and its evolution. In his series of lectures, he discussed development of numbers and importance of Pigeon Hole Principle. He also discussed irrationality of V2 and gave many different proofs of it. Also he discussed how to approximate v2. On other day he talked about i. Prof. I. K. Rana discussed a geometrical approach to approximate y using sequences. He also discussed intrinsic property of sequence and Cauchy sequence. In his concluding lecture, he discussed nested interval property, model of growth and decay, limit and continuity, properties of continuous functions, tangent to the curve, and differentiability.

Second lecture was on metric space and we are fortunate to have Dr. Tanvi Jain from ISI Delhi to enlighten us with the concepts of arithmetic mean, Frechet mean of m points. She took some informative examples of metric spaces like metric on Hyperspace, Hausdorff metric on CL(X), metric induced by operator norm, Bures-Wasserstein metric, orthogonal Procrustes problem, Wasserstein mean, Polar decomposition. In her subsequent lectures she discussed compactness, sequentially compact and limit point compactness. To make her talk more informative she discussed tutorial sheet comprising of variety of problems. In her last lecture, she discussed the proofs of some famous theorems like Arzela-Ascoli theorem, Implicit function theorem, Picard's existence theorem, Peano's theorem, Banach fixed point theorem and its applications, Fredholm's second integral equations and linear Volterra integral equations and Stone-Weierstrass theorem.

Prof. V. D. Sharma from IIT Bombay delivered a beautiful lecture series on partial differential equations and its geometrical interpretation. He also discussed quasilinear and non-linear partial differential equations with examples. Further he discussed Cauchy's problem and wave equation with their properties. On other day, he delivered a lecture on first order and second degree ODEs. He discussed linear and non-linear ODEs. Further, he explained various methods of solving first order and second degree ODES like variable separable, integrating factor method and he also talked about exact differential equations. In the series of his lectures, he defined different types of solutions of ODEs as general solution, singular solution and particular solution. Subsequently, he discussed envelope of family of solutions as singular solutions and other geometrical interpretation of solutions of ODEs. On his last lecture, he discussed Initial Value Problem (IVP) and Boundary Value Problem (BVP), asymptotic behaviour of IVP and BVP and their applications in real world.

Prof. Mani Mehra from IIT Delhi delivered the lecture on partial differential equations (PDEs). On her series of lectures, she discussed the classification of second-order partial differential equations in two independent variables. Further, she discussed several physical models (heat equations, wave equations and potential equations) to explain the partial differential equations. PDEs are classified into elliptic, parabolic and hyperbolic. This classification is defined by transforming the PDEs into canonical forms. Further, she talked about partial differential equations in n independent variables and discussed its classification using eigenvalue of the matrix associated with PDEs.

In her subsequent lecture, she discussed the existence, uniqueness, and stability of the partial differential equations. She defined well-posed and ill-posed problems. PDEs are called as well-posed if i. solution exists ii. solution should be unique, and iii. solution depends continuously on initial and boundary data of the problems This is called Hadamard principle of well-posedness of partial differential equations. She elaborated some ill-posed problems and explained its occurrence in nature as Inverse problems. She explains the difficulty in dealing with ill-posed problems. Well-posed are nice to handle and have nice stability features. Several numerical methods are available in the literature to deal with such problems. In her last talk, she discussed the analytical behaviour of heat equations. She explained the finite difference approximation of heat problems. She defined the consistency, stability to define the convergence of finite difference scheme. She uses Fourier's method to show the stability of this problem. At last, she explained the various norms to measure the error while discretizing the continuous problems. She defined maximum norm I. and l, norms and their importance.

Dr. Vivek from DTU delivered useful and informative lectures and lab sessions on "Maxima". He enlightened us with the basic commands of Maxima and their uses in solving ODE/PDE. Then he continued his lecture with the discussion of various famous problems and models like Logistic equation, Lake pollution problem, SIR model, SI model and SEIR model.

Dr. Mukund Madhav Mishra from Hansraj College of University of Delhi who discussed the existence and convergence of Fourier series involving! the notion of Weierstrass approximation theorem, Taylor series, Riesz product, Convolution and Fejer's theorem. In his second lecture, he discussed various problems of mathematics with the audience.


 Time Table

  Time-table (with names of speakers and tutors):

Day Date Lec 1
9:30
to
10:30
Tea
10:30
to
11:00
Lec 2
11:00
to
12:00

Lec 3
12:00
to
1:00

Lunch
1:00
to
2:00
Lec 4
2:00
to
3:00
Tea
3:00
to
3:30
Discu / Lab
3:30
to
4:30
Tea
4:30
to
5:00
    Speaker   Speaker Speaker   Speaker   Speaker  
Tue 24-7-2018 Inder K. Rana   Inder K. Rana Inder K. Rana   Tanvi Jain   Tanvi Jain  
Wed 25-7-2018 Inder K. Rana   Inder K. Rana Inder K. Rana   Mani Mehra   Tanvi Jain  
Thu 26-7-2018 V.D Sharma   V.D Sharma V.D Sharma   Tanvi Jain   Vivek
Kumar
 
Fri 27-7-2018 Tanvi Jain   V.D Sharma V.D Sharma   V.D Sharma   Vivek
Kumar
 
Sat 28-7-2018 Tanvi Jain   V.D Sharma V.D Sharma   V.D Sharma   Vivek
Kumar
 
Sun 29-7-2018 Mani Mehra   Mani Mehra Mukund M.
Mishra
  Mukund M.
Mishra
  Mukund M.
Mishra
Valedictory
Session

Name of the tutors/Lab Session

Sr.n Name Affiliation
1 Dr. Vivek Kumar Delhi Technological University
2 Dr. Tanvi Jain ISI, Delhi
3 Dr. Mukund Madhav Mishra Hansraj College,University of Delhi

 


 

List of actual Participants

Sr. SID Full Name Gender Affiliation Position in College / Univ. Univ./ Insti. M.Sc./M.A. Year of Passing M.Sc./ M.A Ph.D. Deg.
Date
1 21677 Dr Bhagwan Singh Male Government Girls Degree College Asst. Professor Aligarh Muslim University Aligarh 2005 10/31/2014
2 21717 Ms Shipra Chauhan Female University of Delhi Research Scholar University of Delhi 2012  
3 21721 Ms Prachi Sachan Female Department of Mathematics University of Delhi Research Scholar IIT Kharagpur 2016  
4 21722 Dr. Bhavneet Kaur Female Lady Shri Ram College for Women Assistant Professor University of Delhi 2002 11/19/2016
5 21729 Dr. Manisha Aggarwal Female St. Stephen's College Assistant Professor Hindu College, University of Delhi 2012 11/6/2016
6 21767 Ms. Shalini Rana Female Ambedkar University Delhi MPhil Amity University 2016  
7 21769 Mr. Harendra Verma Male University of Lucknow, Lucknow. Phd University of Lucknow, 2015  
8 21785 Mr Akmal Raza Male Jamia Millia Islamia Ph.D. Student Jamia Millia Islamia 2014  
9 21802 Mr Akber Ali Khan Male Jamia Millia Islamia Research Scholar Jamia Millia Islamia New Delhi 2011  
10 21805 Dr. Seema Bansal Female Swami Shraddhanand College Associate Professor Delhi University 1988 3/14/2014
11 21809 Dr. Sucheta Nayak Female Lady Shri Ram College for Women Asst. Prof. MSc 2005 5/4/2018
12 21826 Ms. Chanchal Garodia Female Jamia Millia Islamia PhD Student University Of Delhi 2014  
13 21831 Dr. Vandana Rajpal Female Shivaji college Asst. Prof. IIT Delhi 2009 5/31/2015
14 21836 Mr. Mohd Rafiq Male University of Delhi Ph.D. Student University of Delhi 2016  
15 21837 Dr. Dinesh Kumar Male Deen Dayal Upadhyaya College, University of Delhi Assistant Professor Hindu College, University of Delhi 2009 8/9/2016
16 21873 Ms. Chhavi Mangla Female Jamia Millia Islamia Ph.D. Scholar M.A. Mathematics (University of Delhi) 2011  
17 21875 Mr. Vinod Kumar Male Jamia Millia Islamia PhD student CCS University Meerut 2006 6/25/2016
18 21878 Mr. Sajan Aggarwal Male Jamia Millia Islamia, New Delhi PhD Scholar IIT Delhi 2014  
19 21896 Dr. Rakesh Batra Male Hans Raj College, Delhi University Assistant Professor Department of Mathematics, University of Delhi 2002 12/14/2016
20 21897 Dr. Amit Mittal Male Atmaram  Sanatan Dharma College Assistant Professor Hans Raj College, Delhi University 2002 11/24/2010
21 21899 Dr. Anju Dhall Female G.G.D.S.D college,affilated to M.D.U ,Rohtak Assistant Prof M.D.U,Rohtak 2002 7/1/2015
22 21901 Mr Kapil Shekhar Male Dayalbagh Educational institute PhD Dayalbagh Educational institute 2010  
23 21910 Mr. Om Prakash Meena Male Department of Mathematics, University of Delhi PhD Research Scholar M.Sc. , Hansraj college, University of Delhi 2017  
24 21914 Mr. Pardeep Kumar Male SPM College Assistant Professor University of Delhi 2005  
25 21916 Dr. Lakhveer Kaur Female Jaypee Institute of Information Technology (JIIT) Asst. Prof. Panjab University 2008 11/14/2013
26 21928 Ms. Seema Lata Gupta Gupta Female School of Mathematics, Devi Ahilya University Ph.D. Reaserch Schalor School of Mathematics, Devi Ahilya University, Indore 2006  
27 21934 Mrs. Charanpreet Kaur Female SGTB KHALSA Asst. Prof. University of Delhi 1996  
28 21951 Dr. Santosh Kaushik Female Bhagini Nivedita College Assistant Professor St. Stephens College, Delhi University 2004  
29 21958 Dr. Jyoti Darbari Female Lady Shri Ram College Assistan Professor MSc, University of Delhi 1996 6/12/2018
30 21960 Ms. Monika Arora Female Miranda House Assistant Professor University of Delhi   10/3/2016
31 21971 Ms. Shivani Sharma Female Ambedkar University Delhi Mphil Student Hansraj College, University Of Delhi 2016  
32 21975 Dr Pooja Arora Female Shyama Prasad Mukherji College for Women, University of Delhi Assistant Professor University of Delhi 2004 5/30/2015
33 21981 Ms. Apeksha Verma Female Miranda House Assistant Professor University of Allahabad 2008  
34 21982 Dr. Namita Sharma Female Dyal Singh College (University of Delhi) Assistant Professor St. Stephen's College 2012 8/29/2017
35 21984 Dr. Durvesh Kumar Verma Male Miranda House Assistant Professor BHU 2008 9/20/2014
36 21985 Mrs. Mridu Sharma Female Department of mathematics, Delhi University Ph.d. student Miranda house, DU 2015  
37 21990 Dr Preeti Jain Female Atmaram  Sanatan Dharma College ASSISTANT PROFESSOR MAHARISHI DAYANAND UNIVERSITY, ROHTAK, HARYANA 2004 6/11/2009
38 21993 Ms. Anjali Upadhyay Female University of Delhi PhD Banaras Hindu University 2015  
39 21998 Dr. Sarla Devi Bhardwaj Female Dr. Bhim Rao Ambedkar College, University of Delhi Associate Professor university of delhi 1987 12/1/1993
40 21999 Ms. Deepti - - Female Shivaji College Asst.Prof. Panjab University, Chandigarh 2007  
41 22000 Ms. Krishma Babbar Female University of Delhi Student St. Stephen’s College, University of Delhi 2014  
42 22001 Ms. Adiba Naz Female University of Delhi MPhil M.Sc. Mathematics, Hansraj College, University of Delhi 2016  
43 22003 Ms Shalu Yadav Female Delhi University MPhil Student Lucknow University 2016  
44 22007 Ms. Sarita Kumari Female University of Delhi PhD University of Delhi 2017  
45 22017 Mr Pravata Kumar Behera Male ARSD College, University of Delhi Assistant Professor Sambalpur University 2000  
46 22022 Ms. Ramanpreet Kaur Female University Of Delhi PhD University Of Delhi 2017  
47 22029 Assist Pro Ruchika Jain Female Dr Akhilesh Das Gupta Institute Of Engineering And Technology Assistant Professor Ccs University, Meerut 1999 2/16/2016
48 22042 Ms Pushali Trikha Female Jamia Millia Islamia Research Scholar UNIVERSITY OF DELHI 2013  
49 22044 Mr. Lone Seth Jahanzaib Male Jamia Millia Islamia Research Scholar Jamia Millia Islamia 2015  
50 22045 Ms Nasreen . Female Jamia Millia Islamia PhD Scholar Kirori Mal College, University of Delhi 2014  
51 22046 Ms Uzma Nigar Female Jamia Millia Islamia Phd scholar 7.9 2015  
52 22047 Mr. Lalit Kumar Som Male Motilal Nehru College Assistant Professor C.C.S. University, Meerut, U.P. 2012  
53 22049 Mr. Rahul Singh Male Ramanujan College (University of Delhi) Assistant Professor Ch. Charan Singh University Meerut UP 2007  
54 -- Mr. Arvind Male Hans Raj College, Delhi University        
55 -- Dr. Megha Agarwal Female Ramanujan College (University of Delhi)        
56 -- Mr. Deepak Kumar Male Ramanujan College (University of Delhi)        

 


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