Differential Equations - Theory and Applications (2022)

Convener(s)


Name:	Dr. S Saravanan	Dr. R Rakkiyappan	Dr. Venky Krishnan
Mailing Address:	Professor and Head Department of Mathematics, Bharathiar University, Maruthamalai Road, Coimbatore - 641046	Assistant Professor Department of Mathematics Bharathiar University, Coimbatore 641 046	Associate Professor TIFR Centre for Applicable Mathematics Sharada Nagar, Chikkabommasandra, Post bag No.6503, Bangalore 560 065
Email:	sshravan at buc.edu.in	rakkiyappan.maths at buc.edu.in	vkrishnan at tifrbng.res.in

Differential Equations arise naturally while modeling physical phenomena. It is very important and extremely difficult to determine whether a physical problem is stated correctly. Even when this is fixed, closed form solutions are rarely possible which could otherwise serve as vital sources of intuition. Hence we do find approximate solutions to such equations arising in real life problems. The objective of the proposed school is to highlight the essential basic theory for finding analytical solutions of important differential equations and their applications in various other fields such as mechanics. Differential Equations form an integral part of curriculum in any postgraduate course in Mathematics. The topics to be covered in the school are arranged in such a way that the university and college teachers get exposed to a good mix of classical theory and modern approaches.

Dates:

Tuesday, August 16, 2022 - 16:45 to Monday, August 29, 2022 - 18:30

Venue:

Bharathiar University

Venue Address:

Department of Mathematics,
Bharathiar University,
Coimbatore 641 046

Venue State:

Tamil Nadu

Venue City:

Coimbatore

PIN:

641046

Chrono Order:

404

Syllabus:

Syllabus to be covered :

Name of the Speaker with affiliation	Lectures No.of	Detailed Syllabus
Ali Hyder, Reader, TIFR CAM (AH)	4	Laplace equation: Method of separation of variables, fundamental solution for Laplace equation, mean value properties, maximum principles, solution to the Poisson equation, regularity of solutions to the Laplace equation, analyticity of solutions to the Laplace equation, Harnack inequality, Green function, explicit computation in certain domains, representation formula for the boundary value problem for Laplace equation using Green function, energy methods for the Laplace equation.
Girija Jayaraman, Former Professor, IIT Delhi (GJ)	4	Models in Physics and Natural Sciences: Modelling perspective and history of model develolpment using differential equations, Initial/Boundary value problems in Physics and Natural Sciences, forced and free oscillations, Physiological applications involving wave/pulse propagation, Mathematics of Diffusion, Diffusion in Ecology, Ecological applications using nonlinear dynamical systems, Challenges in solving Pysico- Biological models with multi-scales.
G D Veerappa Gowda, Professor, TIFR CAM (GDVG)	4	First order PDEs: Transport equation, solving linear, semilinear, quasilinear and fully nonlinear first order equations by the method of characteristics. Physical and real-world applications of these PDEs.
P Kandaswamy, Former Professor, Bharathiar University (PK)	4	Applications of IBVPs: ode model - human immune system, system of equations, phase plane analysis and interpretation, two extreme cases; pde models - gravity waves and their occurrence in atmosphere, critical levels and their significance, the energy and momentum transfer; double diffusive convection and its solutions, finger and other instabilities.
P S Datti, Former Professor, TIFR CAM (PSD)	4	Wave equation: d'Alembert formula (dimension n=1), spherical means and Euler- Poisson-Darboux equation, explicit construction of the solution in odd dimensions, and for even dimensions by the method of descent, energy methods, explanation of finite speed of propagation for solution to the wave equation.
Venky Krishnan, Associate Profesor, TIFR CAM (VK)	4	Heat equation: Introduction to the heat equation and derivation of the fundamental solution using Fourier transforms, finding a solution to the standard homogeneous initial value problem with appropriate initial conditions as well as solution to the non-homogeneous problem by Duhamel's principle, regularity of solution to the heat equation in bounded domains and explanation of the infinite speed propagation, Space analyticity of solutions to the heat equation, counterexample describing lack of space-time analyticity for solutions to the heat equation, heat mean value formula, weak and strong maximum principles, energy methods

Names of the tutors with their affiliation:

Divyansh Agrawal, TIFR CAM (DA)
Dr N Raja, KPR College of Engineering (NR)
Dr S Meenasaranya, PSG Arts College (SM)
Soumen Senapati, TIFR CAM (SS)
Swaraj Paul, TIFR CAM (SP)

Time Table:

Tentative time-table:

Day	Date	FN Session 1 (9.30–11.00)		FN Session 2 (11.30–1.00)		AN Session 1 (2.30–3.30)		AN Session 2 (4.00-5.00)
Tue s	16 Aug ‘22	Lecture GJ		Lecture PK	L	Tutorial GJ+SM+NR		Tutorial PK+SM+NR	S
Wed	17 Aug ‘22	Lecture GDVG	T	Lecture GJ	U	Tutorial GDVG+DA+SS	T	Tutorial GJ+SM+NR	N
Thu	18 Aug ‘22	Lecture PK	E	Lecture GDVG	N	Tutorial PK+SM+NR	E	Tutorial GDVG+DA+SS	A
Fri	19 Aug ‘22	Lecture GJ	A	Lecture PK	C	Tutorial GJ+SM+NR	A	Tutorial PK+SM+NR	C
Sat	20 Aug ‘22	Lecture GDVG		Lecture GJ	H	Tutorial GDVG+DA+SS		Tutorial GJ+SM+NR	K
Sunday : Off
Mon	22 Aug ‘22	Lecture PK		Lecture GDVG		Tutorial PK+SM+NR		Tutorial GGDVG+DA+SS	S
Tue	23 Aug ‘22	Lecture AH		Lecture VK	L	Tutorial AH+DA+SS		Tutorial VK+SS+DP	N
Wed	24 Aug ‘22	Lecture PSD	T	Lecture AH	U	Tutorial PSD+SS+SP	T	Tutorial AH+DA+SS	A
Thu	25 Aug ‘22	Lecture VK	E	Lecture PSD	N	Tutorial VK+SS+SP	E	Tutorial PSD+SS+SP	C
Fri	26 Aug ‘22	Lecture AH	A	Lecture VK	C	Tutorial AH+SS+SP	A	Tutorial VK+SS+SP	K
Sat	27 Aug ‘22	Lecture PSD		Lecture AH	H	Tutorial PSD+SS+SP		Tutorial AH+SS+SP	S
Sunday : Off
Mon	29 Aug ‘22	Lecture VK		Lecture PSD		Tutorial VK+SS+SP		Tutorial PSD+SS+SP

Selected Applicants:

Sr.n	SID	Full Name	Gender	Affiliation	Position in College /University	University/ Institute M.Sc./ M.A.	Year of Passing M.Sc./ M.A	Ph.D.Deg Date
1	41721	Dr Avijit Sarkar	Male	University of Kalyani	Teacher	University of Kalyani	2002	03/02/2010
2	41723	Mr. Subhodip Ghosh	Male	Visvabharati University	PhD	Visvabharati University	2021
3	41736	Mr. Amit Kumar Verma	Male	MNNIT Allahabad	PhD Scholar	MNNIT Allahabad	2015
4	41771	Mr Bajarang Lala Pawar	Male	RMD Sinhgad School of Engineering,Warje-Pune	Assistant Professor	Savitribai Phule Pune University, Pune.	2019
5	41773	Mr. Firdous Ahmad Mala	Male	GDC Sopore	Assistant Professor
6	41787	Mr. Yashveer Kumar	Male	Indian Institute of Technology (Banaras Hindu University), Varanasi, India.	PhD Student	MNNIT ALLAHABAD	2016
7	41801	Mr Tamizhazhagan S	Male	National Institute of Technology	PhD	Pondicherry University	2018
8	41810	Dr. Gopal Kumar Gupta	Male	TEERTHANKER MAHAVEER UNIVERSITY MORADABAD UP INDIA	Assistant Professor	Banaras Hindu University	2011	15/03/2019
9	41815	Mr Nawaj Sarif	Male	Aliah University	PhD	University of Delhi	2017
10	41826	Ms. Dona Alex	Female	NATIONAL INSTITUTE OF TECHNOLOGY TIRUCHIRAPPALLI	PhD	Pondicherry University	2019
11	41838	Mr Rock Ramesh	Male	St.Josephs University, Bangalore	Assistant Professor	St.Joseph's College Trichy	2006	22/04/2022
12	41860	Mrs. Girija Muniyappan	Female	Vellore Institute of Technology, Vellore	Ph.D.	Government Thirumagal Mills College, Gudiyattam	2019
13	41881	Mr. Parveen Kumar	Male	IIT JAMMU	JRF	VISVESVARAYA NATIONAL INSTITUTE OF TECHNOLOGY NAGPUR	2020
14	41911	Mr. Jyoti Turi	Male	Visva Bharati (A central university)	Ph.D.Scholar	Visva Bharati (A central university)	2020
15	41946	Ms Ilavarasi R	Female	ERODE ARTS AND SCIENCE COLLEGE	PhD.	M.sc.	2017
16	41964	Dr. Deepak Sarma	Male	Assam Agricultural University	Assistant Professor	B.Borooah college under Gauhati University	2014	14/10/2019
17	41965	Dr Raghunath Kodi	Male	Bheema Institute of Technology and Science	Assistant Professor	RAYALASEEMA UNIVERSITY	2011	19/12/2019
18	41969	Mr Bala Samuvel J.	Male	Alpha Arts and Science College	Assistant Professor	M.Sc	2012
19	41972	Dr. Tamilmani Jambu	Female	PSG College of Arts & Science	Assistant Professor	Sri Sarada College for Women (Autonomous), Salem-16	2014	26/07/2021
20	41977	Ms. Sudha Y	Female	National Institute of Technology Tiruchirappalli	Research Scholar	Bharathiar University	2010
21	41991	Ms Poornima P	Female	National Institute of Technology Tiruchirappalli	PhD	Bharathiar Univeristy\ Maharaja's College for Women	2006
22	42088	Ms. Madhvi Raj	Female	Nit Delhi	PhD	Patna University	2019
23	42109	Mrs Bharathi Vadivelu	Female	P. T. Lee Chengalvaraya Naicker College of Engg. and Tech.	Assistant Professor	Annamalai	2003
24	42119	Mr Anish Kumar	Male	National Institute Of Technology Jamshedpur	PhD	Central University of South Bihar	2018
25	42128	Mr. N. S. Gopal	Male	Birla Institute of Technology and Science Pilani Hyderabad Campus	PhD	Bangalore University	2017
26	42150	Mr. Arunkumar M	Male	National Institute of Technology Tiruchirappalli	PhD Student	PSG college of arts and science, Coimbatore	2021
27	42155	Mr. Manikandan S	Male	Sri Ramakrishna Mission Vidyalaya College of Arts and Science	PhD Research Scholar	Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020.	2021
28	42163	Mr Vargees Kaviyan E	Male	Sri Ramakrishna Mission Vidyalaya College of Arts and Science	PhD Research Scholar	Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore.r	2021
29	42166	Mr. Shubham Garg	Male	IIT Jodhpur	PhD	IIT Ropar	2019
30	42190	Mr. Vijayakumar M	Male	SRM Institute of Science and Technology	Research Scholar	University of Madras/ M.Sc.	2016
31	42213	Dr. Abdur Raheem	Male	Aligarh Muslim University	Assistant Professor	Aligarh Muslim University	2006	13/11/2013
32	42245	Mr. Jyotiranjan Nayak	Male	SRM UNIVERSITY	PhD	Sambalpur University	2020
33	42250	Mr. Pashupati Nath Prasad	Male	IIT Delhi	M.Sc passed out Student	IIT Delhi	2021
34	42255	Mr. Pawan Kumar Shaw	Male	National Institute of Technology Jamshedpur	PhD	MSc in Mathematics & Computing	2016
35	42279	Mr. Guddu Kumar	Male	T. P. COLLEGE MADHEPURA	Asst. Prof.	IISER KOLKATA	2014
36	42285	Dr. Divya A	Female	Sri Ramakrishna college of Arts & Science	Assistant Professor	Madurai Kamaraj University	2013	12/05/2021
37	42321	Dr. Swati Agarwal	Female	Mangalayatan University	Assistant Professor	St. John's College (Dr. Bhimrao Ambedkar University), Agra	2011	11/01/2019
38	42332	Mr. Sanowar Ahasan	Male	NIT JAMSHEDPUR	PhD	Visva-Bharati University	2020
39	42339	Mr. Chalapati Rao Medikonda	Male	aditya college of engineering	Asst.Prof.	acharya nagarjuna university	2006
40	41974	Mr. B M Tamilzharasan	Male	Erode Arts and Science College	PhD	Erode Arts and Science College	2017

Local Participants
	T. Elizabeth Jeyanthi	PhD student, Department of Mathematics Bharathiar University
	M. Manimekalai	PhD student, Department of Mathematics Bharathiar University
	R. Muthu Meena	PhD student, Department of Mathematics Bharathiar University
	R.Surendar	PhD student, Department of Mathematics Bharathiar University
	S. Sridhar	PhD student, Department of Mathematics Bharathiar University
	V. Navaneethakrishnan	PhD student, Department of Mathematics Bharathiar University
	J.V. Brainy	PhD student, Department of Mathematics Bharathiar University
	T.N. Parthasarathy	PhD student, Department of Mathematics Bharathiar University
	S. Pragathi	PhD student, Department of Mathematics Bharathiar University
	T. Maniratinam	PhD student, Department of Mathematics Bharathiar University
	R. Saranya	PhD student, Department of Mathematics Bharathiar University
	P. Gokul	PhD student, Department of Mathematics Bharathiar University
	S. Shanmugasundaram	PhD student, Department of Mathematics Bharathiar University
	R Gokilam	PhD student, Department of Mathematics Bharathiar University
	R Thanamani	PhD student, Department of Mathematics Bharathiar University

How to Reach:

TBA

School Short Name:

deta

School Type:

IST