Explores the core concepts of Brownian motion, from molecules to cells, including its history, hypothesis versus description, Langevin's solution, and methods for measuring Brownian motion.
Explores the Hamiltonian formalism for the harmonic oscillator, focusing on deriving Lagrangian and Hamiltonian, isolating the system, and generating new conserved quantities.
Explores the history, mathematical models, and experimental techniques of Brownian Motion, revealing its molecular nature and significance in cell biology.
Explores heat diffusion, temperature distribution, and thermal equilibrium in complex systems using the heat equation and Jupyter Notebook simulations.
Explores solving diffusion equations in steady state conditions for concentric spheres with fixed concentration and flux, emphasizing the importance of linearity and homogeneity.
Explores Stochastic Differential Equations with examples like Brownian Motion and Square-Root Processes, discussing their relation to Partial Differential Equations.
