 One way to look at the difference between calculus and all math prior to calculus is that pre-calculus mathematics focuses on what things are Well calculus focuses on how things are changing So in geometry we want to find the area perimeter and volume of a rectangle Well, maybe not the volume but in calculus we want to find how the area changes as the perimeter changes So we need to talk about change In general the amount of change is the amount at the end minus the amount at the start For example a town's population grew from 30,000 to 80,000. What was the population change? Now it's important to keep in mind you should always include units Since the numbers represent population the implied units are persons 30,000 persons 80,000 persons And so the change was the population at the end minus the population at the start 50,000 persons and so we say the town's population changed by 50,000 persons We often use words that indicate a direction of change For example if a quantity goes from 4 to 10 the change is the amount at the end minus the amount to the start That's 10 minus 4 or 6 And so we could say that it has changed by 6 or we could also say that it has increased by 6 What if the quantity goes from 10 to 4? So again the change is the amount at the end minus the amount at the start and here that change is negative 6 Now we could say that the quantity decreased But an important rule never never never never never never Mix a direction with a sign so we can say that it has changed by negative 6 or we can say it has decreased by 6 no sign So for example a car's speed went from 75 miles per hour to zero miles per hour And let's describe its speed change in two ways Now a mile is an archaic unit of distance used only in Liberia, Myanmar and one other country whose name escapes me So the speed change is the speed at the end minus the speed at the start So that's a zero minus 75 or negative 75 miles per hour And so we could say the speed changed by negative 75 miles per hour Or we could say the speed Decreased and remember never mix signs with directions So decreased is a direction got less and so we should say decreased by 75 miles per hour Now while the amount of change is important We need more a car's speed can decrease by 75 miles per hour over a distance of 300 feet By applying the brakes or within one hundredth of a second By crashing we want the change of one quantity with respect to another quantity and we'll look at that next