Calculus – the word itself will scare most people away from it. We often shy away from things we don’t understand or comprehend. We start liking something when we begin to have an idea of what that thing is. The objective of this article is to help us get a glimpse of what calculus is and what it does to us.
We are not going to study how to solve calculus. We are not even going to learn the meaning of the big words, or sometimes they can be considered scary words, like the derivative, the integration, the limit, the function, and any other words we use to study calculus. For this specific study, we will focus on how calculus is affecting us in our lives.
Even though we won’t study how to calculate calculus, we need to identify the two basic parts of calculus. The two foundations of calculus are the differential calculus and the integral calculus (don’t let the words scare you away!). This is why we have part 1 in the title because we will be looking at differential calculus in this study.
Have you ever tried playing with your friends or family the game “breath-holding contest,” either underwater or just sitting around holding your breath? Each of us has the capability to hold our breath, but we differ in how long each of us can do it. This is because we have different bodies, sizes of lungs, ages, experiences, and even heartbeats. All these things and a few more factors will affect how long we can hold our breath. “How does this connect with differential calculus?” you may ask. All these factors can be translated into a calculus formula, and we can determine how long each of us can hold our breath. This is how scientists determine at what depth a human being can hold his or her breath when that person dives underwater.
Have you ever wondered how the parts of commercial airplanes stay in place with the speed they are traveling, the sound energy that the engines are producing, and the weight they are carrying with the thin pressure in the atmosphere? These things are calculated with the help of differential calculus. The materials used on airplanes are subjected to different tests and that is how the breaking point will be determined. The engineers will try different materials to see which one has the stronger capability to endure the different pressures that the material will be exposed to during flight.
It is easy to pick the strongest material for an airplane, but airplane manufacturers also need to consider the cost of these materials because nobody will buy an airplane that is too costly for airline companies to buy and maintain. Calculus can again be applied with this problem. They can select the cheaper material that can withstand the trials of flight.
The goal of differential calculus is to find the limit of something but not to reach that limit. With these examples, we already saw how differential calculus was used by determining the limits of each problem. We used it in biology, engineering, and economics in the examples mentioned above. Think of other things on which we place a limit but we don’t reach or break that limit. Those things are applying differential calculus in principle.