What the above equation says is that a numerical estimate of the function evaluated at the next time step (i.e. ??(?? ??)) is equal to the function evaluated at the current timestep (i.e. ??(??)) plus the derivative at this current time step times the step magnitude (i.e. ????(??) or said differently, the step size times the slope of the function). This gives us a numerical approximation of the function ??(??) at all time instances into the future that we wish to evaluate. Implementation in MATLAB with an Example: Trying to Catch the Train Oh no! You slept through your alarm and are running late to catch the train to work (again!) The train itself is an automated train and is programmed to travel at a constant speed until it gets ME 240 | WINTER 2024 close to the station. As it gets close to the station, the train is programmed to reduce its speed as a function of position such that: ??(??) = 0.1??(??) where ?? is the train's distance from the station. This allows the train to come to nice and safe stop exactly at the station's location. Take note that the train speed is the same as the