IST - Ordinary Differential Equations and Dynamical Systems (2023)
Speakers and Syllabus
Syllabus:
| Sl No | Name of the speaker and Affiliation |
Topic of lectures | Number of lectures with tutorials |
| 1. | Prof. Rajeev Bhaskaran (RB) ISI Bangalore |
General methods, Existence, uniqueness of solution, Picard'stheorem, Peano's theorem, scalar differential equations, system of differential equations, differential and integral inequalities, fixed point methods, linear systems, properties of linear homogeneous systems, inhomogeneous systems, behaviour of n-th order linear homogeneous equation, asymptotic behaviour. | 6 lectures (9 hours) |
| 2. | Dr. Kamna Porwal(KP) IIT Delhi |
Series solutions, solutions about ordinary points, about singular points, Frobenious series, Laplace transform, Fouriertransform, Application to differential equations, numerical solutions of ODE, Euler methods, Runge Kutta methods, error analysis, Multistep methods | 6 lectures (9 hours) |
| 3. | Dr. Syed Abbas (SA), IIT Mandi |
Stability, stability of linear systems, continuous dependenceand stability properties, linear systems, two dimensionalsystems, stability by Lyapunov method, autonomous and nonautonomous systems. | 6 lectures (9 hours) |
| 4. | Prof. Malay Banerjee (MB) IIT Kanpur |
Mathematical modelling, population dynamics, single speciesmodels, Lotka Volterra models, Infectious disease model, compartmental model, SIR, SEIR models, simulations using matlab multispecies model, nonautonomous systems, persistence, permanence, stability and bifurcation analysis, simulations using Matlab . | 6 lectures (9 hours) |
| 5. | Ganesh Satpute (GS) | Course/Tutorial associates. | 18 hours (6 (S)+12(T)) |
| 6. | Nikhil Chaurasia (NC) | Course/Tutorialassociates | 18hours |
| 7. | Shraddha Salwahan (SS) | Course/Tutorialassociates | 18hours |
| 8. | Shivam Mishra (SM) |
Course/Tutorialassociates | 18hours |
Time Table
Tentative timetable
| Schedule for the first week | |||||||
| Date/Day | 9:30 to 11:00 | Tea Break | 11:30 to 1: 00 | Lunch Break | 3:00 to 4:00 | Tea Break | 4:30 to 5:30 |
| Day1 | RB | RB | T1 RB, GS, SS | T2 RB, GS, SS | |||
| Day2 | RB | RB | T3 RB, GS, SS | T4 RB, GS, SS | |||
| Day3 | RB | RB | T5 RB, GS, SS | T6 RB, GS, SS | |||
| Day4 | KP | KP | T7 KB, GS, SS | T8 KB, GS, SS | |||
| Day5 | KP | KP | T9 KB, GS, SS | T10 KB, GS, SS | |||
| Day6 | KP | KP | T11 KB, GS, SS | T12 GS, SS | |||
| Schedule for the second week | |||||||
| Day7 | SA | Tea Break | SA | Lunch Break | T1 KP, NC, SM | Tea Break | T2 KP, NC, SM |
| Day8 | SA | SA | T3 KP, NC, SM | T4 KP, NC, SM | |||
| Day9 | SA | SA | T5 KP, NC, SM | T6 KP, NC, SM | |||
| Day10 | MB | MB | T7 MB, NC, SM | T8 MB, NC, SM | |||
| Day11 | MB | MB | T9 MB, NC, SM | T10 MB, NC, SM | |||
| Day12 | MB | MB | T11 MB, NC, SM | T12 MB, NC, SM | |||
Legends:
- RB: Prof. Rajeev Bhaskaran
- KP: Dr. Kamana Porwal
- MB: Prof. Malay Banerjee
- SA: Dr. Syed Abbas