Differential Equations - Theory, Modeling, Data Assimilation and Algorithms

Rooted in years of interdisciplinary research and collaboration, the chapters in this book highlight the central role of differential equations in describing how systems evolve across science and engineering while emphasizing the modern need to connect theory with data and computation. It bridges rigorous mathematical foundations with the practical challenges of modeling and inference, demonstrating how data assimilation refines models using observations and how advanced numerical algorithms enable the study of complex systems beyond analytical reach. By addressing the interplay between models, data, and computation, the book equips advanced students, researchers, and practitioners with the understanding and tools needed to apply differential equations meaningfully in contemporary scientific inquiry.