Invited Talk on Differential Equation: Unfolding its Applications
Objectives
To motivate the students to understand the essence of Differential
- To explain the overview of Richness of Differential
- To reach the students through few relevant Applications of differential
Outlines of the Session:
Differential equations guided by laws of
- Modelling simple problems and finding its
- Expression for momentum and work
- Puzzles solved by Srinivasa Ramanujan.
- Deriving Einstein’s Formula E = Mc2, where M =Variable
- Application to Life
- Population Model : Volterra Integral
- Some interesting
- Limitations of Modelling in real
One of the faculty member of PG Department of Mathematics, Mr.Bharatha.K welcomed the gathering and introduced the resource person Prof. R. Ranganrajan and the session was handed to the resource person.
Session started with the motivation that guided by dynamics. He explained simple differential equation and the idea to obtain the solution. Further he applied same idea for few difference equation and explained discrete solutions. He inspired the student to think critically on the application of mathematics in daily life. In particular he gave the incident of Srinivasa Ramanujan solving puzzle in the article “Strand” of England. Continuing he unfolded the logical thinking hidden in our daily routines.
He briefed about the application of differential equations in physics.In par- ticular the dynamics of Boson particles and derived the Einstein‘s formula, which relates energy of a particle having variable mass.
Continuing he explained the notion of momentum and the factors that dic- tates momentum. He gave the overview of the same concepts in wave theory. In particular non linear dispersive and dissipative systems.
Moving on he elucidated the conservation of momentum in the population model by deriving Volterra integral equation which governs the bacterial growth in the ideal situation.
In conclusion he gave insights of differential equation and its applications in ocean engineering, non-linear dynamics and also pointed out some limitations of modelling the system of few real world problems.
