Aditya M. Deshpande
In the previous post, I discussed the basics regarding the stability of fixed points of a dynamical system and explained it with a simple continuous-time one-dimensional example. In this post, I will discuss fixed points for a general case of a continuous-time $n$-dimensional system. Fixed point...
Aditya M. Deshpande
This post contains some of the important notes which come in handy while working with vector-calculus. Vector Space A vector space is a collection of objects called vectors, which may be added together and multiplied/scaled by scalars. Scalars are often taken to be real numbers. \[\mathbf{x} =...
Aditya M. Deshpande
Stability theory is used to address the stability of solutions of differential equations. A dynamical system can be represented by a differential equation. The stability of the trajectories of this system under perturbations of its initial conditions can also be addressed using the stability...