Calculus: History and Usage in Everyday Life

Introduction: As a Computer Science student who never took Pre-Calculus and Basic Calculus in Senior High School, I never realized that there will be a relevance of Calculus in everyday life for a student. Background: Before the beginning of it uses, there’s a short background of the origination of the word “Calculus”. 17th century British Scientist/Mathematician Sir Isaac Newton and German mathematician Gottfried Leibniz coined this term but both had different arguments about the definition of the term which sparked controversy in the late 1600s. Back in the earlier days (mainly the Greek times), Romans use stones just to count for vital purposes and they did by means of an abacus. Mathematicians back in the earlier centuries spend countless days and hours come up with new ideas and inventions just for people to be taught of these facts and solve real-life problems that we need for jobs and especially Mathematics because even Science, Engineering and other specialties require numbers. Topic sentence: There are two fields in calculus: differential and integral. Differential is using more of the function derivatives to study the behavior and rate on different quantity change. It can be graphed, computed, analyzed and processed by normal people once a problem was given. Topic sentence: Integral calculus, on the other side, makes use of anti-derivatives or more likely the reversed process of differentiation. According to one study by Atangana, in Derivative with a New Parameter, 2016, the focus of differential calculus is “derivative of a function, related notions such as the differential, and their applications”. Commentary: It is true that calculus can be applied in daily life situations (e.g. Lesson about Related Rates), we can also look for solutions used from derivatives and other applications of solving corresponding problems. Thesis statement: Although not formally introduced until the Newton-Leibniz theories and controversy, there were Greek Mathematicians involved in the development of Calculus back during Before Christ period. Evidence & citing: Those three Greek mathematicians were Euclid, Archimedes and Apollonius of Perga. The second Greek mathematician here, Archimedes, used infinitesimals despite using it to solve problems regarding areas and volumes rather than tangents and derivatives. It was used in 500s AD, by Indian Mathematics and it is just for the study of moon’s motion. As we go in to the modern world of calculus, which now means as “continuous change”, we have now a continuous change in the society and creating our own mathematical problems like physics problems or any other sort. This essay could get in what more can differential and integral calculus can do for other individuals besides computer science: Differential calculus involves as the study of rate change of quantities. The most perfect example of integrating differential calculus is physics. In physics, there are factors to consider about your independent variable and dependent variable in your problem. Calculus does the same with its mathematical concepts: the independent variable is the one that inputs a function to define quantity manipulated in the given problem. For instance, we can have with x as the weight and y as the velocity. Those two variables will affect the dependent variable which is z, the force that we can deliver from it. Physics and calculus both use mathematical expressions and scientific theories to come up with the solution to the problem. Commentary: Differential calculus can be applied outside of physics but also in temperature checking for weather and business purposes. We all know that integral calculus is the inverse of differentiation but in the more meaningful way of describing this, it studies integrals and properties. Function becomes an anti-derivative/ primitive function of . We can use this kind of calculus to find areas under a curve, from , mass center, kinetic energy, work, and other physics problems related to distance, velocity and acceleration, probability and average value of a function.

Topic sentence: In this portion, here are now some useful ways of involving Calculus: first is a Computer Science specialty: Game Development. Video and computer games are simply used by people just to spend off some time just to discover fascinating ideas, just playing it to take time off workload and academic problems and/or as hobby. At one point, and right now, 3D models which includes multiple variable equations are used to study these because in game development, 3D models, illuminations and physical engines are going to be utilized in creating their games. As a student not having game development and yet has some interest in video games, I looked at the change overtime of the graphics, sounds and action displayed in the video games. Evidence & citing: Spherical harmonics functions are solutions to Laplace Formula if it’s restricted to ONLY a sphere. This may be a scientific term but it can be useful to measuring the graphics and shapes of a person specifically when about to game development in its design proper. For game development, a student of that department has to be very comfortable and adaptable to vectors mainly for mathematics with vectors comprise graphics and computational geometry. This also involves simulations and tests whether one way from a problem could work as a starter or not.

There is another important aspect of game development in Calculus, the evolution of real-life people in video games. In 1999, the graphics were particularly Hulk-like basketball athletes because of the physical built in requirements to their position they play in the sport. Evidence & citing: It also includes people (serving as fans in attendance in the crowd, technical crew, officials or referees and other on-air personnel). Back then, it was a monotonous actions made by the players it’s because game programming was at its beginning stages of development because technology, brighter minds and ideas can change and modify the old actions through Mathematical theories and programming, graphics design and spherical harmonics. It is important that video games are also served as 3D component in the modern day usage of an individual and they expect real-life images and stories displayed. Commentary: As the years go by and with more technological aspects and brighter ideas made up by other people, this NBA2K series made up an idea of including more outstanding graphics and use of mathematical and calculus to create exact body movements and voice-over of real people like doing the exact shooting release of a player and recruiting legitimate broadcasters in the sports journalism industry to do as such. Including in the use of calculus is the programming part of creating video games. People pay attention to the detail in creating an application program in which they can create scenarios and options for a user to pick in to release the information they wanted or whatever they use to get entertained.

Topic sentence: Another department in which calculus is beneficial in the current state of where we are right now is Public Health Improvement. The field of epidemiology (study of infectious diseases spread) requires the field of calculus. The main reasons for this are the following: the people who are mainly targeted by one disease, those who have been infected and recovered. Calculus helps to determine how fast a disease spreads, where it is originated and best ways to treat it along with science. Commentary: In equations used by calculus, it is used to compute the number of infections, infection rate and recovery change in a daily basis. One good example of this scenario happening is the currently still happening COVID-19 pandemic. We all know about its basic information is that it originated in Wuhan where it spreads fast because of the winter weather in China with common colds and coughs are some of the main diseases caused by cold weather. Those were some signs and symptoms but now it includes breathing difficulty, change in gustatory sense (sense of taste) and making contact with other people. In the calculus usage, it started from the spreading of the virus which started in China and then it was spread all throughout the other parts of the world (Europe, Oceania, Africa, The Americas). Evidence & citing: According to a mathematics section of allusesof.com, Calculus was defined as an intended use for the counting of infinitely smaller numbers and it is a calculation of change to help describe the dynamic change of the world. If one person watches the news and looks for updates about the Coronavirus pandemic, they will see the graphics about the number of cases, number of deaths and its rate, infection rate, recoveries and its rate. Some of the biggest institutions like John Hopkins in the United States track down the most essential information recovered from different areas in the world and from reliable news sources and channels to update any positive or negative feedbacks in regarding the tracker of the worldwide Coronavirus cases.

Topic sentence: After discussing a pressing and ongoing concern besides computer science, as a student, I also ponder why computer-related programs like Information Technology and Information Systems have calculus as requirements and on writing this essay, I find out why. It begins with the basic parts of opening a system like “1” or “0” to start and then it gets in to the deeper context. It’s like our brains, technology field and mathematics. Every computer related program has to undergo numerous calculations, predictions and other data gathering and executing methods. We first use calculus in the beginning as pen and papers in solving mathematical equations which require solving for derivatives, functions and requirements of calculus like Maxima and Minima, lowest points, graphing parts, etc. These capabilities can help a student create their own artificial intelligence which can be very good for game developers and programmers to indicate non-playable aspects for a user. Computer-related programs in college create students in which they can create websites, AIs, complex computational models, build responsive websites which can reach on the backend (in which ICS2609 is applicable “Back-End Programming”) and some unapplied mathematics theories can be thrown in once someone gives us a problem in which we don’t know the background of one mathematical problem. Despite the heavy demands (like discrete math/structures, linear algebra, calculus, advanced statistics and probability, data structures, design and analysis of algorithms) that the world is hearing upon technology and computer-related students who would be the next generation of technology, there is a silver lining to what computer scientists have done: digital patient monitoring systems in ICUs for hospitals, emergency rooms and patient care around the world, air traffic control software to minimize accidents which are served with control rooms, speed guns, signals and LEDs, to inform people along with their families, life-saving medications and other health care are made thanks to computer science. One of the things I also found out in the lesson of Related Rates, the science of physics is widely used in a majority sense. This is used to calculate measurements like acceleration and velocity using derivatives and time as factors but every problem would be given out based on what’s needed. Different and multiple sciences and computer-related aspects are required and/or combined by human will through countless numbers of hours and days to compute different problems to grasp individual demands and requirements in which an organization is looking for to improve the success of one project and also include finding more research, brainpower and critical thinking on in the inside of one individual to cope up with what complicated problems can be solved.

Conclusion paragraph: To summarize everything in the essay, back before Leibniz and Newton even came up with calculus, it was even the Romans getting in involved for what’s vital for them to learn something new. I learn something new as well, calculus wasn’t just one branch of mathematics, but it was a true life saver for us humanity. This helped computer scientists with the technology to give comforts to people in everyday lives, hospitals to track and monitor if a person’s life is in jeopardy or not from various ailments, and giving a way for video game enthusiasts and (hopeful and professional) game developers to come up with better designs and graphics on solving problems which can be improved upon. One example of the last the NBA2K video game evolution. Technology has improved with the help of people learning the basic calculus, pre-calculus and advanced calculus. It may be hated at all by people and a difficult course to master but in the end, something good will come up in the future that requires one of these topics covered in Calculus for work to be done and solving everyday demands.

References

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