Jacobians

A Jacobian is a mathematical tool that describes how a change in one set of variables leads to a change in another set—much like a map showing how a small shift in input points to a corresponding shift in output. It’s especially useful in calculus and physics for transforming coordinates or understanding how functions stretch, shrink, or skew space. Think of it as a detailed guide that captures how little changes ripple through a system, helping to analyze and manipulate complex relationships between variables efficiently and accurately.