Convener(s)
| Name: | Prof. Rakesh Kumar Bajaj | Prof. Syed Abbas | Dr. Bidhan Chandra Sardar |
| Mailing Address: | Professor & HoD Department of Mathematics Jaypee University of Information Technology |
Professor & Dean SRIC & IR Indian Institute of Technology, Mandi |
Assistant Professor Department of Mathematics, IIT Madras |
| Email: | rakesh.bajaj at juitsolan.in | abbas at iitmandi.ac.in | bidhan.math at iitm.ac.in |
This NCMW aims to introduce the participants to the advanced topics in Ordinary differential equations & Partial Differential Equations (PDEs) related to the Dynamical Systems and Applications to Control Systems. This will be indeed immensely helpful to the researchers who are already familiar with the basics of ODEs & PDEs, since we are going to discuss several state-of-the art techniques related to stability, controllability etc. for the dynamical systems and control systems.
In the first week, we plan to discuss topics like linear systems, solutions, fundamental matrix, autonomous and nonautonomous systems, Stability of systems, equilibrium, Lyapunov stability At the end of the first week, we plan to focus more on Controllability of Differential Equations & Differential Inclusions: Dynamical systems & Control systems, Controllability, Observability, stability, differential inclusions.
In the second week, weak solutions of PDEs: Elliptic, Parabolic & Hyperbolic problems along with Controllability for ODEs & PDEs will be discussed. Controllability of Hyperbolic PDEs and Hilbert uniqueness method and Controllability of Parabolic PDEs with Carleman estimates will be covered by the end of the week.
Prerequisites for the Workshop: The participants should have the fundamental knowledge of Linear Algebra, real analysis and familiarity with both ordinary differential equations (ODEs) and partial differential equations (PDEs), as these form the basis for rigorous analysis in dynamical systems and modelling.
Dates:
Venue:
Venue Address:
Jaypee University of Information Technology
Waknaghat (Shimla Hills), Distt – Solan, Himachal Pradesh – 173 234
Venue State:
Venue City:
PIN:
Syllabus:
| Name of the Speakers with their affiliation. | No. of Lectures (1.5 Hours each) | Detailed Syllabus |
| Prof. Syed Abbas (IIT Mandi) | 6 SAS | Existence and uniqueness, linear systems, solutions, fundamental matrix, autonomous and nonautonomous systems, Stability of systems, equilibrium, Lyapunov stability |
| Dr. Dwij N Pandey (IIT Roorkee) | 6 DNP | Controllability of Differential Equations & Differential Inclusions: Dynamical systems & Control systems, Controllability, Observability, stability, differential inclusions and controllability of differential inclusions; ; Experience with tools like MATLAB or Python for modelling and simulating dynamical and control systems. |
| Dr. Mani Mehra (IIT Delhi) | 6 MMA | Numerical methods for solving IVPs for ODEs: Difference equations, Single step methods: Taylor series method, explicit Runge-Kutta Methods, convergence, order, relative & absolute stability. Multistep methods: Development of linear multistep method using interpolation and undetermined parameter approach, convergence, order, relative and absolute stability |
| Dr Tanmay Sarkar (IIT Jammu) | 6 TSR | Existence of weak solutions of heat and wave equations via Galerkins method, Energy estimates for heat and wave equations. Uniqueness of weak solutions. |
| Prof A K Nand Kumaran (IISc Bangalore) | 6 NKR | Introduction to Controllability for ODEs & PDEs, Observability Inequality, Controllability of wave equation. Hilbert uniqueness method. |
| Dr. Bidhan Chandra Sardar (IIT Ropar) | 6 BCS | Controllability of the heat equation, Observability, Stabilizability, Carleman estimate for the Heat equation, Null Controllability for the Heat equations, |
| Tutors: | ||
| Mr. Shivam Mishra | (SM) | (IITMandi), |
| Mr. Deeksha Srivastava | (DS) | (IITRoorkee) |
| Mr. Ritu Raj | (RR) | (IITRopar) |
| Ms. Swati Garg | (SG) | (IITRopar) |
References:
- Shair Ahmad, M. Rama Mohana Rao, Theory of ordinary differential equations: withapplications of biology and engineering, Affiliated East-West Private Lmt., New Delhi [India], ©1999
- Morris W. Hirsch, Stephen Smale and Robert L. Devaney, Differential Equations, DynamicalSystems, and an Introduction to Chaos, Third Edition, 2013, Elsevier.
- Stephen Lynch, Dynamical Systems with Applications using MATLAB, Second Edition, 2014, Birkhäuser Cham
- Earl A. Coddington and Norman Levinson; Theory of Ordinary Differential Equations, , Krieger Publishing Company,
- David F. Griffiths, Desmond J Higham; Numerical Methods for Ordinary Differential Equations (IVPs), Springer.
- Uri M. Ascher and Chen Greif, A First Course in Numerical Methods, PHI
- J D Lambert, Computational Methods in ODEs, John Wiley & Sons, NY, USA.
- L.C. Evans, Partial Differential Equations, AMS.
- S. Micu and E. Zuazua, An introduction to the Controllability of Partial Differential Equations, Lecture notes.
- A. K. Nandakumaran, Exact controllability of Linear Wave Equations and Hilbert Uniqueness Method, Proceedings, Computational Mathematics, Narosa (2005).
Time Table:
Tentative time-table, mentioning names of the speakers and tutors with their affiliation:
| WEEK – I (9th June 2025 – 14th June 2025) | |||||||||
| Day | Date | Lecture 1 (9.30– 11.00) |
Tea (11.05– 11.25) |
Lecture 2 (11.30– 1.00) | Lunch (1.05– 1.55) |
Lecture 3 (2.00–3.30) |
Tea (3.35- 3.55) |
Tutorial Discussion (4.00-5.00) | Snacks (5.05- 5.35) |
| (Speaker) | (Speaker) | (Speaker) | (Tutor) | ||||||
| Mon | 9th June, 2025 | SAS | DNP | MMA | SAS + SM | ||||
| Tues | 10th June, 2025 | SAS | DNP | MMA | DNP + DS | ||||
| Wed | 11th June, 2025 | SAS | DNP | MMA | SAS + SM | ||||
| Thu | 12th June, 2025 | SAS | DNP | MMA | DNP + DS | ||||
| Fri | 13th June, 2025 | SAS | DNP | MMA | MMA + SM | ||||
| Sat | 14th June, 2025 | SAS | DNP | MMA | MMA + DS | ||||
| WEEK – II (16th June 2025 –21st June 2025) | |||||||||
| Day | Date | Lecture 1 (9.30– 11.00) | Tea (11.05– 11.25) | Lecture 2 (11.30– 1.00) | Lunch (1.05– 1.55) | Lecture 3 (2.00–3.30) | Tea (3.35- 3.55) | Tutorial Discussion (4.00-5.00) | Snacks 5.05- 5.35 |
| (Speaker) | (Speaker) | (Speaker) | (Tutor) | ||||||
| Mon | 16th June, 2025 | BCS | NKR | TSR | BCS + RR | ||||
| Tues | 17th June, 2025 | BCS | NKR | TSR | BSC + RR | ||||
| Wed | 18th June, 2025 | BCS | NKR | TSR | TSR + SG | ||||
| Thu | 19th June, 2025 | BCS | NKR | TSR | NKR + RR | ||||
| Fri | 20th June, 2025 | BCS | NKR | TSR | TSR + SG | ||||
| Sat | 21st June, 2025 | BCS | NKR | TSR | NKR + SG | ||||
Selected Applicants:
| Serial | SID | Full Name | Gender | Affiliation | Position in College/University | University/Institute M.Sc./M.A. | Year of Passing M.Sc./M.A |
| 1 | 62139 | Ms. Pooja Airan | Female | Malaviya National Institute of Technology | PhD | Guru Jambheshwar University of Science andTechnology, Hisar | 2020 |
| 2 | 62142 | Ms Chhaya Midha | Female | Malaviya National Institute of Technology Jaipur | Research Scholar | Central University of Punjab Bathinda | 2020 |
| 3 | 62310 | Mr. Vajahat Karim Khan | Male | Aligarh Muslim University | Research Scholar | Aligarh Muslim University, Aligarh | 2019 |
| 4 | 62313 | Mr. Javed Akhtar | Male | Aligarh Muslim University | PhD | Aligarh Muslim University | 2021 |
| 5 | 62430 | Mr. Rajveer Singh | Male | Central University of Punjab | Research Scholar | University of Delhi | 2022 |
| 6 | 62492 | Mr. Akash Panwar | Male | The LNM Institute of Information technology | PhD Student | The LNM Institute of Information Technology | 2021 |
| 7 | 62494 | Mr. Tanmoy Majumdar | Male | IIT (ISM), Dhanbad | PhD | University of Kalyani | 2021 |
| 8 | 62495 | Mr. Neelesh Kumar | Male | Indian Institute of Technology (ISM) Dhanbad | PhD | Vikram University, Ujjain | 2022 |
| 9 | 62545 | Ms. Kanwalpreet Kaur | Female | Eternal University, Baru Sahib (Himachal Pradesh) | PhD scholar | M.Sc (Honours) Mathematics, Akal University, Talwandi Sabo (Punjab) | 2022 |
| 10 | 62546 | Mr Muthuraj T | Male | Indira Gandhi Centre for Atomic Research | PhD | Bharathiar University | 2018 |
| 11 | 62576 | Dr. Abhinav Kumar | Male | IIT Bombay | Postdoctoral Researcher | Central University of South Bihar, Gaya | 2018 |
| 12 | 62651 | Mrs Sivaranjani Ramasamy | Female | KPR Institute of Engineering and Technology | PhD Research Scholar | Bharathiar University/ Government Arts College/ M.Sc | 2006 |
| 13 | 62652 | Mr. Senthilprabu T | Male | KPR Institute of Engineering and Technology | PhD Research Scholar | Bharathiar University/ PSG College of Arts and Science / M.Sc | 2005 |
| 14 | 62783 | Mr. Gaurav Kumar Goyal | Male | Malaviya National Institute of Technology Jaipur | PhD | Institute M.Sc. | 2023 |
| 15 | 62841 | Mr. Manoj Sheoran | Male | Banasthali Vidyapith | Research Scholar | Maharshi Dayanand University, Rohtak | 2020 |
| 16 | 63050 | Ms. Parul Kaushik | Female | Banasthali vidyapith rajasthan | PhD | M.Sc. | 2023 |
| 17 | 63182 | Ms. Monika Monika | Female | Thapar Institute of Engineering and Technology | Ph.D | Kurukshetra University | 2019 |
| 18 | 63188 | Ms Sukirtha M | Female | Bharathiar University | PhD student | M.Sc | 2022 |
| 19 | 63200 | Ms Reena Choudhary | Female | NIT Raipur | Research Scholar | Atal Bihari Vajpayee University Bilaspur | 2021 |
| 20 | 63262 | Ms Amisha Rani | Female | National Institute of Technology Kurukshetra | PhD | Kurukshetra University | 2021 |
| 21 | 63305 | Mr. Akram Khan | Male | Indian institute of technology Roorkee | phD | Indian institute of technology kharagpur | 2024 |
| 22 | 63324 | Mr. Harsh Tiwari | Male | Indian Institute of Technology Roorkee | PhD | Banaras Hindu University | 2024 |
| 23 | 63551 | Mr. Debabrata Mandal | Male | INDIAN INSTITUTE OF TECHNOLOGY ROORKEE | PhD | Visva-Bharati (A Central University) | 2022 |
| 24 | 63919 | Mr. Sabarish Kumar V | Male | Bharathiar University | Ph.D Research Scholar | M.Sc., Mathematics CA | 2021 |
| 25 | 63983 | Ms Pooja Rani | Female | Thapar Institute of Engineering and Technology, Patiala | PhD | Guru Nanak College, Sri Muktsar Sahib, Punjab | 2019 |
| 26 | 64083 | Mr Anil Kumar Sahni | Male | IIT ROORKEE | Phd scholar | Central University of jharkhand | 2021 |
| 27 | 64169 | Ms. Aswathi A P | Female | National Institute of Technology Goa | PhD | CENTRAL UNIVERSITY OF KERALA | 2024 |
| 28 | 64201 | Mr. Deepjyoti Kalita | Male | Indian Institute of Technology Roorkee | PhD | GAUHATI UNIVERSITY | 2021 |
| 29 | 64247 | Ms. Aleena Thomas | Female | Indian Institute of Space Science and Technology | Research Scholar | University of Kerala | 2020 |
| 30 | 64520 | Mr. Sukanta Halder | Male | PDPM Indian Institute of Information Technology, Design and Manufacturing, Jabalpur | PhD Student | Ramakrishna Mission Vidyamandira | 2019 |
| 31 | 64834 | Ms Aashi Aggarwal | Female | Banasthali Vidyapith | Research Scholar | M.Sc | 2023 |
| 32 | 64887 | Dr. Ramandeep Kaur | Female | Guru Nanak Dev University | Assistant Professor | Guru Nanak Dev University, Amritsar | 2006 |
| 33 | 64902 | Mr. Muniyasamy M | Male | National Institute of Technology Karnataka | PhD Student | M.Sc at Pondicherry University | 2019 |
| 34 | 64956 | Mr. Ahmad Faraz Razi | Male | ALIGARH MUSLIM UNIVERSITY | PhD | ALIGARH MUSLIM UNIVERSITY M.Sc. | 2019 |
| 35 | 62338 | Mr Bharathkumar N | Male | National Institute of Technology Puducherry | PhD | Ramakrishna Misssion Vivekananda College, Chennai | 2021 |
| 36 | 63504 | Mr. Harichandan Nayak | Male | NIT Andhra Pradesh , Tadepalligudem, India. | PhD | M.Sc. | 2021 |
| 37 | 64442 | Mr Remington L | Male | Central University of Tamil Nadu | PhD Scholar | Loyola College, Chennai. | 2024 |
| 38 | 64209 | Ms. Kanchan Kanchan | Female | University of Delhi | PhD Scholar | Miranda House College,University of Delhi | 2023 |
| 39 | 64481 | Dr. Suraj Goyal | Male | J. C. Bose University of Science and Technology, YMCA | Assistant Professor | M.Sc. (Hons. School) Mathematics, Department of Mathematics, Panjab University Chandigarh | 2010 |
| 40 | 62250 | Mr. Sarabindu Dolui | Male | National Institute of Technology Andhra Pradesh | PhD | B.H.U. | 2018 |
| 41 | 65128 | Ms. Kausika Chellamuthu | Female | Bharathiar University (Last place of study) | PI (last held position) | Bharathiar University | 2012 |
| 42 | 64883 | Dr. Shubham Jaiswal | Male | PGDAV College, University of Delhi | Assistant Professor | Kumaun University, Nainital | 2011 |
| 43 | 62297 | Mr Sombir Dhaniya | Male | Central University of Punjab | PhD | Kurukshetra University Kurukshetra | 2019 |
| 44 | 64882 | Mr. Rahaman Ali | Male | Indian Institute of Technology Patna | PhD | University of North Bengal | 2019 |
| 45 | 62372 | Mr. Dinesh Indrajmal Kumawat | Male | Indian Institute of Technology Roorkee | PhD | University of Mumbai | 2019 |
| 46 | 63459 | Ms. Shuchi Sahu | Female | National Institute of Technology Raipur | PhD | Center for Basic Sciences, Pt. Ravishankar Shukla University, Raipur, C..G | 2022 |
| Local Participants | |||||||
| 1 | 62359 | Master Ritesh Gupta | Male | Jaypee University of Information technology | PhD | Himachal Pradesh University M.sc | 2018 |
| 2 | 62432 | Mr. Pradyumn . | Male | Jaypee university of information and technology, Waknaghat | Ph.D | Himachal Pradesh University (H.P.U.) | 2022 |
| 3 | 62537 | Mr. Manish Kumar | Male | JUIT | PhD | JUIT | 2023 |
| 4 | 65078 | Mr. Nitish Thakur | Male | Himachal Pradesh University, Shimla | PhD | Himachal Pradesh University, Shimla | 2020 |
How to Reach:
How to Reach (https://www.juit.ac.in/contact/location)
JUIT Waknaghat is midway between Shimla & Solan . Shimla is 24 Kms from the campus. Kalka is the nearest broad gauge railway station. Waknaghat is very well connected with buses from Delhi, UP, Haryana, Punjab, Rajasthan and Chandigarh/Kalka.
Waknaghat is 24 kms. from Solan on the way to Shimla on NH-22. For coming to JUIT, one has to take a left turn at Waknaghat and drive for 3 kms. From JUIT, Shimla is 24 kms. The location is at a height of 1550 m above MSL.
TEMPERATURE – Max. 35°C (Summer) Min. – 2°C (Winter)
CLOTHING: Cotton clothes in Summer and heavy woolens in winter.
LANGUAGE: Hindi, English are understood and spoken by the people .
About Himachal
Surrounded by the purple blue hue on the mountains and spread across seven hills in the Himalayas with steep forested hillsides, long winding roads, bustling bazaars and a glorious past, Shimla – The capital city of Himachal Pradesh is spell binding. Visit Shimla any time of the year and the historic hilly town is never shy of happy vacationers. Not only known for its landscapic beauty, the city has been growing into an educational hub. From prestigious schools like Bishop Cotton and Auckland House, to colleges like HPU and St. Bede’s, the city speaks volumes of the knowledge it has stored. Jaypee University of Information Technology (JUIT), centred between the two major cities, Shimla and Solan has grown profoundly in the past decade. The serenity, the calmness of the environment gives an internal boost and pump to your learning skills. All you need to do is, feel the air, gaze upon the lush landscapes and sing the song of your life. Also when the time comes to bid adieu to this place with heaps of knowledge, tonnes of happy memories and a heavy heart.
How to reach JUIT:
By Road:
There is good connectivity of the campus with major cities around. It lies three kilometres away from the national highway. HRTC, Haryana and Punjab Roadways buses along with private travellers are easily available from Shimla as well as Chandigarh. They drop you off at Waknaghat from where cab service till the campus are available 24*7 all around the year.
By Train:
The nearest broad gauge railway station is Chandigarh or Kalka from where buses, and taxis are available. It takes approx 2 hours by road to Waknaghat
By Air:
The convenient all season airport is Chandigarh from where buses, taxis are available to Waknaghat . It takes approx 2.5 hours to JUIT.
Since Shimla is a tourist place, therefore, it is advised to all the participants that they should book their tickets as early as possible to avoid summer rush.