TEW Differential Equations, Mathematical Modelling and Analysis (2018)
Venue:  Deshbandhu College, Delhi, Delhi 
Date:  24th, Jul 2018 to 29th, Jul 2018 
Name  Prof. Abhay Bhatt  Ms. Harindri Chaudhary 
Mailing Address 
Indian Statistical Institute Delhi 
Associate Professor Department of Mathematics 
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.

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, BuresWasserstein 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 ArzelaAscoli 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 StoneWeierstrass 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 nonlinear 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 nonlinear 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 secondorder 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 wellposed and illposed problems. PDEs are called as wellposed 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 wellposedness of partial differential equations. She elaborated some illposed problems and explained its occurrence in nature as Inverse problems. She explains the difficulty in dealing with illposed problems. Wellposed 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
Timetable (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 
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  2472018  Inder K. Rana  Inder K. Rana  Inder K. Rana  Tanvi Jain  Tanvi Jain  
Wed  2572018  Inder K. Rana  Inder K. Rana  Inder K. Rana  Mani Mehra  Tanvi Jain  
Thu  2672018  V.D Sharma  V.D Sharma  V.D Sharma  Tanvi Jain  Vivek Kumar 

Fri  2772018  Tanvi Jain  V.D Sharma  V.D Sharma  V.D Sharma  Vivek Kumar 

Sat  2872018  Tanvi Jain  V.D Sharma  V.D Sharma  V.D Sharma  Vivek Kumar 

Sun  2972018  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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