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|
Indian Statistical Institute Delhi
Associate Professor Department of Mathematics
Speakers with their affiliations:
Name of the speaker
|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|
|Name of the Speaker with affiliation||No. of Lectures||Detailed Syllabus|
|Prof. V.D. Sharma
|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
|6||From Rationals to reals, understanding limits, from Riemann integration
to Lebesgue integration.
|Dr. Tanvi Jain
Metric spaces - examples, sequences, continuity, complete and compact metric spaces.
|Prof. Mani Mehra
|3||Classification of second order PDEs. Complete study of one
dimensional parabolic equation.
|Dr. Mukund Madhav Mishra
University of Delhi
|1||Fourier Series and its convergence.|
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 (with names of speakers and tutors):
|Discu / Lab
|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
|Fri||27-7-2018||Tanvi Jain||V.D Sharma||V.D Sharma||V.D Sharma||Vivek
|Sat||28-7-2018||Tanvi Jain||V.D Sharma||V.D Sharma||V.D Sharma||Vivek
|Sun||29-7-2018||Mani Mehra||Mani Mehra||Mukund M.
Name of the tutors/Lab Session
|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.
|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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