Differential Equations – Theory and Applications (2022)
Venue: | Bharathiar University, Coimbatore, Tamil Nadu |
Date: | 16th, Aug 2022 to 29th, Aug 2022 |
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) |
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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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