The Initial Value Problem

An Initial Value Problem (IVP) is a type of mathematical question where you want to find a function that describes how something changes over time or space, given its starting state. Essentially, you know its initial conditions (for example, the starting position and speed of a ball), and your goal is to determine how it behaves afterward. This involves solving differential equations that relate the function to its rate of change. IVPs are common in physics, engineering, and other sciences to predict future behavior based on initial measurements.