NCMW - Analysis of Dynamical Systems and Applications to Control Systems (2025)
Speakers and 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 | ||||