For all its mystique, calculus is simply advanced algebra and geometry. Familiar rules of geometry and algebra are slightly altered so they can be used to solve more complicated problems. This article series will use Mark Ryan’s Calculus For Dummies as its guide.Suppose you have a man pushing a crate up a consistently straight incline. You have to determine how much energy is needed to push the crate to its top. In this case, the individual is pushing the box up the hill with an unchanging force. Thus, the crate is pushed up at a consistent speed. Ordinary physics formulas and math can be used to determine how many calories are needed to get the crate to the top of the incline.
Suppose, however, that the hill is curved. This would entail that the curve is changing. Its increments, furthermore, are not consistent; with each push, the force with which the box is pushed, changes. More profoundly, the energy expended changing for every single instant. That is, it is not changing every second, every thousandth, every ten thousandth or every millionth of a second, but constantly changing each instant. Thus, calculus is the mathematics of change. Ordinary rules of math are applied to problems that evolve and continually change.
In the case of physics, on the one hand, formulas remain the same when looking at a curving incline. This means that the algebra and trigonometry that you use remain the same. However, what makes this distinct to the incline problem, is that you must break up the curving incline problem into smaller pieces. Each component is solved separately. Provided you zoom in ar enough, the length of the incline of the curve is basically straight. Since it is straight, you can solve this part of the problem just as you would a problem involving a straight incline. Indeed, in calculus you take problems that are incapable of being solved with regular math because things are constantly changing and zooms in on curves until the curves are straight. Then you simply use regular math to solve the problem.
What makes calculus such a curiosity is that it zooms in infinitely. Indeed, calculus resolves around the concept of infinity. The reason for this is that i something is constantly changing, from one instant to the next, it is changing infinitely often, with each infinitesimal moment different from the next. Suppose you are measuring the length of a buried cable. This cable runs diagonally from one corner of a park to the other. Calculus can be used to find its length if it is hung between two towers such that its shape is that of a catenary.
This is an example of a real-world example in which calculus can be used. You can also use calculus to determine the area of a roof that is complex and non-spherical. This is obviously something an architect needs to be able to do. Remember how regular math can be used to calculate speeds that are constant or consistent? Well, scientists needed calculus to calculate how to get Viking I to Mars because Earth and Mars travel on elliptical orbits. This means that they travel in different shapes. furthermore, the speeds of both planets are continually changing, to say nothing of how gravitational pulls of the relevant astronomical bodies.