Differential Fields

Differential fields are mathematical structures that combine elements of algebra and calculus. Essentially, they consist of a set of elements (like numbers or functions) along with a special operation called differentiation, which measures how these elements change. Just like how ordinary fields (like the real numbers) allow for addition and multiplication, differential fields allow for differentiation. This framework is useful in studying how quantities change over time and is essential in fields like physics and engineering, where understanding change is crucial. They offer a rigorous way to analyze dynamic systems mathematically.