# There to know the rate of change and

There are many branches of mathematics that are existing nowadays and one of these includes calculus, which is also categorized into two; the differential calculus and integral calculus. Differential calculus deals with computing or finding the derivatives of the functions to be able to know the rate of change and the behaviour the function. On the other hand, integral calculus deals with integrals to be able to determine the areas, volumes, and lengths. As we use and study calculus, it made me wonder who discover or invented it. And as I did my research, I found out that there were two people who were known when we are talking about the discovery and history of calculus namely Sir Isaac Newton and Gottfried Wilhelm von Leibniz. These two are great mathematician who contributed a lot in the field of calculus but if you are going to ask who discovered calculus, the answer is still unclear because calculus is discovered by many people over centuries. The idea and some concept of calculus is already present during Greek times. During ancient Greek times, Eudoxus a Greek mathematician used the method of exhaustion (one thinks of the areas measured expanding so that they account for more and more of the required area), a precursor to limits in order to calculate area and volume. Then Archimedes continued Eudoxus’ idea and invented heuristic, the same with integration in order to calculate area. Even though the idea of who should take credit in discovering calculus is still unclear many people just credited Newton and Leibniz since they made their own discoveries independently that led us to what we know as calculus. Newton discovered the inverse relationship between the integral ( the area beneath the slope of a curve) and the derivative ( slope of the curve ), which made him consider as the creator of calculus. Newton idea of calculus is that the application of calculus were geometrical and is related to the physical world, such as describing the orbit of the moon around the earth. For Leibniz, calculus was more about understanding and analysis of change in graphs. Even though they are different from each other, Leibniz’s discovery was just as important as Newton’s. There are many applications of calculus in our everyday life specially in each profession like architecture, engineering, medical field, etc. In architecture, calculus is used not just to enhance the design of structures but also to make it a successful and durable one . In engineering, numerous part of structural building require math for it to be accurate just like for example in hydrology, the volume is calculated as the area under the curve of flow versus time and is accomplished using calculus. In my everyday life, aside from answering calculus exam and questions which obviously need the concept of calculus, there are also things that I do that involves calculus. To start with, the first application of calculus in my life is when I travel every Friday from Ateneo de Zamboanga University to my home in Ipil Zamboanga Sibugay. In traveling, my father usually fetch me from school which is approximately 130 km away to our home. Using calculus I can eventually know what is the possible time that I’ll reach home. Of course considering the time I left here and the speed of the vehicle. I father driving speed is usually 32 km/hr therefore I will reach home at approximately 4 hours. Another application of calculus is when I am reading a webtoon (an app with stories), I can usually can read at a rate of 5 chapters per hour. So using calculus you can immediately know what is the approximate number of chapters I can read in a certain number of time. Let say for example I start reading at 5 pm to 7 pm, by using the data that is already given which is 5 chapters per hour, to find the number of chapters I’ve read you just need to multiply 5 to the number of hours I spend reading which is two hours. Therefore, the 5 x 2 = 10 chapters I’ve read for two hours.Lastly is using the concept of calculus in the air conditioner at the classroom. Example I set my desired room temperature at 25 degrees celsius . Assume that the current room temperature in class is 30 degrees celsius. This is what we so called the Proportional Integral Derivatives controller. The temperature in the room will not go down immediately but slowly and until it will reach my desired room temperature. We may not understand the concept of calculus easily and without us knowing, we are already applying in in our everyday life we still need to be thankful because of it’s discovery. Studying and understanding it well will lead us to a better understanding of this subject. Even things like throwing something includes the concept of calculus with us not being aware of it.