Explore the Smoluchowski equation's application in modeling aggregation and fragmentation phenomena in this informative lecture. Delve into the mathematical framework used to describe the dynamics of particle size distributions in various physical and chemical systems. Gain insights into how this equation captures the essential features of coalescence and breakup processes, and learn about its relevance in fields such as atmospheric science, polymer chemistry, and colloidal systems. Discover the analytical and numerical techniques employed to solve the Smoluchowski equation and understand its limitations and extensions.