👉 The dominant mathematical framework in modern science and engineering is undoubtedly
differential equations
, which describe how quantities change over time or space. These equations capture relationships between variables and their rates of change, making them essential for modeling dynamic systems in physics, biology, economics, and beyond. They underpin everything from predicting population growth to simulating fluid flow, leveraging calculus (especially ordinary and partial derivatives) and linear algebra to analyze and solve complex, real-world problems. While linear algebra, probability, and statistics also play critical roles, differential equations remain the cornerstone for modeling continuous change and interactions.