Lectures related to Tests of Invariance in Polynomial Equations

Complex Numbers: Operations, Polar Form, and Solutions

Covers operations on complex numbers, polar coordinates, and polynomial solutions.

Homogeneous Linear Second-Order Differential Equations

Covers the solution of homogeneous linear second-order differential equations with constant coefficients and explores various cases of real and complex roots.

Maximum Entropy Principle: Stochastic Differential Equations

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

Factorisation: The Fundamental Theorem of Algebra

Covers the Fundamental Theorem of Algebra, polynomial division, and complete factorization of complex polynomials.

Equations: Degree and Solutions

Explores polynomial equations, their degree, solutions, and domain definition.

Parametric Curves: Envelope and Caustics

Explores parametric curves, focusing on finding envelopes and caustics.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.