Differential Equations – Theory and Applications (2022)

Venue:	Bharathiar University, Coimbatore, Tamil Nadu
Date:	16th, Aug 2022 to 29th, Aug 2022

School 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

List of the actual speakers:

List of the actual tutors:

Syllabus:

Actual syllabus covered by each speaker:

Name of the Speaker with affiliation	No. of Lectures	Detailed Syllabus
Ali Hyder, 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, 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, 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, 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, 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, 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

Time Table

Actual time-table that was followed during the programme:

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	16 Aug ‘22	Lecture GJ		Lecture PK	L	Tutorial GJ+MM+NR		Tutorial PK+MM+NR
Wed	17 Aug ‘22	Lecture GDVG	T	Lecture GJ	U	Tutorial GDVG+DA+SP	T	Tutorial GJ+MM+NR
Thu	18 Aug ‘22	Lecture GJ	E	Lecture GDVG	N	Tutorial GJ+MM+NR	E	Tutorial GDVG+DA+SP
Fri	19 Aug ‘22	Lecture GJ	A	Lecture GDVG	C	Tutorial GJ+MM+NR	A	Tutorial GDVG+DA+SP
Sat	20 Aug ‘22	Lecture GDVG		Lecture PK	H	Tutorial GDVG+DA+SP		Tutorial PK+MM+NR
Sunday : Off
Mon	22 Aug ‘22	Lecture PK		Lecture AH		Tutorial PK+MM+NR		Tutorial AH+DA+SP
Tue	23 Aug ‘22	Lecture AH		Lecture VK	L	Tutorial AH+DA+SP		Tutorial VK+DA+SP
Wed	24 Aug ‘22	Lecture PSD	T	Lecture AH	U	Tutorial PSD+DA+SP	T	Tutorial AH+DA+SP
Thu	25 Aug ‘22	Lecture VK	E	Lecture PSD	N	Tutorial VK+DA+SP	E	Tutorial PSD+DA+SP
Fri	26 Aug ‘22	Lecture PK	A	Lecture VK	C	Tutorial PK+MM+NR	A	Tutorial VK+DA+SP
Sat	27 Aug ‘22	Lecture PSD		Lecture AH	H	Tutorial PSD+DA+SP		Tutorial AH+DA+SP
Sunday : Off
Mon	29 Aug ‘22	Lecture		Lecture		Tutorial		Tutorial
		VK		PSD		VK+DA+SP		PSD+DA+SP

Names of the tutors with their affiliation:

Divyansh Agrawal, TIFR CAM, Bangalore (DA)
M Meenasaranya, PSG CAS, Coimbatore (MM)
N Raja, KPR IET, Coimbatore (NR)
Swaraj Paul, TIFR CAM, Bangalore (SP)

List of actual Participants

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	41771	Mr Bajarang Lala Pawar	Male	RMD Sinhgad School of Engineering,Warje-Pune	Assistant Professor	Savitribai Phule Pune University, Pune.	2019
3	41787	Mr. Yashveer Kumar	Male	Indian Institute of Technology (Banaras Hindu University), Varanasi, India.	PhD Student	MNNIT ALLAHABAD	2016
4	41801	Mr Tamizhazhagan S	Male	National Institute of Technology	PhD	Pondicherry University	2018
5	41815	Mr Nawaj Sarif	Male	Aliah University	PhD	University of Delhi	2017
6	41826	Ms. Dona Alex	Female	NATIONAL INSTITUTE OF TECHNOLOGY TIRUCHIRAPPALLI	PhD	Pondicherry University	2019
7	41911	Mr. Jyoti Turi	Male	Visva Bharati (A central university)	Ph.D.Scholar	Visva Bharati (A central university)	2020
8	41946	Ms Ilavarasi R	Female	ERODE ARTS AND SCIENCE COLLEGE	PhD.	M.sc.	2017
9	41977	Ms. Sudha Y	Female	National Institute of Technology Tiruchirappalli	Research Scholar	Bharathiar University	2010
10	41991	Ms Poornima P	Female	National Institute of Technology Tiruchirappalli	PhD	Bharathiar Univeristy\ Maharaja's College for Women	2006
11	42119	Mr Anish Kumar	Male	National Institute Of Technology Jamshedpur	PhD	Central University of South Bihar	2018
12	42128	Mr. N. S. Gopal	Male	Birla Institute of Technology and Science Pilani Hyderabad Campus	PhD	Bangalore University	2017
13	42150	Mr. Arunkumar M	Male	National Institute of Technology Tiruchirappalli	PhD Student	PSG college of arts and science, Coimbatore	2021
14	42190	Mr. Vijayakumar M	Male	SRM Institute of Science and Technology	Research Scholar	University of Madras/ M.Sc.	2016
15	42213	Dr. Abdur Raheem	Male	Aligarh Muslim University	Assistant Professor	Aligarh Muslim University	2006	13/11/2013
16	42245	Mr. Jyotiranjan Nayak	Male	SRM UNIVERSITY	PhD	Sambalpur University	2020
17	42279	Mr. Guddu Kumar	Male	T. P. COLLEGE MADHEPURA	Asst. Prof.	IISER KOLKATA	2014
18	42332	Mr. Sanowar Ahasan	Male	NIT JAMSHEDPUR	PhD	Visva-Bharati University	2020
19	41974	Mr. B M Tamilzharasan	Male	Erode Arts and Science College	PhD	Erode Arts and Science College	2017
20		Mr Shafeequdheen P		SRM University, kuragallu, amaravathy, Andhra Pradesh, 522502	Research Scholar
21		Dr. Tamilmani Jambu		PSG College of Arts & Science Coimbatore Tamil Nadu India PIN: 641014	Assistant Professor
22		Dr. Divya A		Sri Ramakrishna college of Arts & Science Coimbatore, Tamil Nadu, India, PIN: 641006	Assistant Professor
23		Ms Nandhini Rajendran		PSG College of Arts & Science Coimbatore, Tamil Nadu, India, PIN: 641014	Assistant Professor
24		Mr. Manikandan S		Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore PIN: 641020	Research Scholar
25		Mr Vargees Kaviyan E		Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore PIN: 641020	Research Scholar
26		T. Elizabeth Jeyanthi		Bharathiar University, Coimbatore	Research Scholar
27		M. Manimekalai		Bharathiar University, Coimbatore	Research Scholar
28		R. Muthumeena		Bharathiar University, Coimbatore	Research Scholar
29		S. S. Mohanrasu		Bharathiar University, Coimbatore	Research Scholar
30		S. Sridhar		Bharathiar University, Coimbatore	Research Scholar
31		V. Navaneethakrishnan		Bharathiar University, Coimbatore	Research Scholar
32		J.V. Brainy		Bharathiar University, Coimbatore	Research Scholar
33		T.N. Parthasarathy		Bharathiar University, Coimbatore	Research Scholar
34		S. Pragathi		Bharathiar University, Coimbatore	Research Scholar
35		T. Manirathinam		Bharathiar University, Coimbatore	Research Scholar
36		R. Saranya		Bharathiar University, Coimbatore	Research Scholar
37		P. Gokul		Bharathiar University, Coimbatore	Research Scholar
38		S. Shanmugasundaram		Bharathiar University, Coimbatore	Research Scholar
39		R Gokilam		Bharathiar University, Coimbatore	Research Scholar
40		R Thanamani		Bharathiar University, Coimbatore	Research Scholar

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