Weak formulation is a way of describing the behavior of a system using the principles of calculus. It involves writing out a mathematical equation that describes how a system works and how it changes over time. The equation uses two main parts: a differential equation, which tells us how a system moves through space, and an integral equation, which tells us how a system changes over time. For example, if you wanted to predict how water moves through a river, you might use a weak formulation, which combines the two equations to give you the answer.