What if, in the future, I want to enter into the career of video game design, specifically programming? In that case, at some point, I will build a physics engine, and to do that, calculus is a must. Higher levels of calculus focus on vectors, which will help me produce objects that move correctly in a game. No one wants to play a game where you throw a ball forwards and then the ball goes backwards. Calculus can also determine the growth rate of something, how much material a building will require, and even the trajectory and velocity measurements required by space mission. In order to have enough experience to apply calculus to these real world problems, I must attend calculus classes at my college, which I currently am as Calculus II, and understand what is taught in the class. In order for me to succeed in a Calculus II class or in a field of work that requires advanced mathematics, experience with foundation level mathematics, the ability to seek assistance for problems so that I do not fall behind, and creative thinking in order to solve problems more efficiently and effectively become a necessity. Experience with the types of mathematics that precede Calculus II will allow me to advance in the class much more smoothly. Calculus I and Algebra are the foundation for Calculus II, and without a strong foundation, there would be nothing I could stand on. These supporting pillars include trigonometric identities, knowing how to derive and integrate functions, and how to simplify complex functions into ones that is easier to understand. An example of a problem that arises with a weak foundation might be a student who enters an Advanced Robotics class without having any previous experience with robotics and fails the class because... ... middle of paper ... ...ways to use existing formulas to do things such as, develop a physics engine for a game or create an algorithm that finds where a sequence of whole numbers exists in pi. Ten years from now, if a career involving calculus is what I elect to pursue, I will flash back on this period in my life as the time I realized how versatile calculus truly is and how I could seize full advantage of it. If I were to employ these techniques to my use of calculus, either in the classroom or in a career that requires it, my endeavors in those fields will come easier and be more successful, than if I allow myself to slack and don’t push myself to utilize them. I will also have a higher chance of enjoying myself in my chosen career and not even considering it work. I might even come to love calculus with the sheer amount that I will discover regarding it through those three techniques.
Would it not be awesome if we could do the things one can only dream of doing? Imagine a world where you can be a running back in the NFL, a powerful sorcerer, and Batman, all in the same day. This world does exist and its the world of video games. Video games allow us to escape reality and the stress that comes with it. It is a world of infinite possibilities with something for everyone. You can slay huge aliens with your friends in a virtual reality, harvest the crops from you very own virtual farm, or even run your own country! In the world of video games, you can do whatever your heart desires! But video games have not always been this way and have not always been around. It has taken a lot of innovation, creativity, and technology to get to where we are today.
lesser of the math evils), and the dreaded, unspeakable others: mainly trigonometry and calculus. While
Key Changes in the Video Game Industry The first wave of home video games was launched nearly 30 years ago. By the early 1980s, this electronic entertainment medium had emerged as a cultural phenomenon, thanks to classics such as Asteroids, Centipede, Donkey Kong, and Pac-Man. The world of video games has, of course, changed drastically since then. For starters, Microsoft, Nintendo, and Sony are now the key players in the console industry, having replaced Atari, Coleco, and Mattel for those top spots. Advances in technology are making game worlds more realistic and interactive than ever before.
My first opportunity to use math outside the academic world was in my part time job with United parcel Service. It was an eye-opener for me in that mathematical techniques, in combination with computers, could be used for solving very complicated real-life problems, such as predicting and controlling the continuos flow of 300 million packages per day. I was deeply impressed by the numerical masterpieces of Jim Gilkinson and Dick Marga, the project managers. They led the way in showing how one could overcome some serious limitations of computers for solving linear systems of equations.
The concept of irrational numbers and their usage makes the topic more interesting to me. Moreover, Euler e is one irrational number which is equal to its derivative and integral. Math has surrounded the world with calculation and there we have
Mathematics is part of our everyday life. Things you would not expect to involve math
Many years ago humans discovered that with the use of mathematical calculations many things can be calculated in the world and even the universe. Mathematics consists of many different operations. The most important that is used by mathematicians, scientists and engineers is the derivative. Derivatives can help make calculations of anything with respect to another event or thing. Derivatives are mostly common when used with respect to time. This is a very important tool in this revolutionary world. With derivatives we can calculate the rate of change of anything with respect to time. This way we can have a sort of knowledge of upcoming events, and the different behaviors events can present. For example the population growth can be estimated applying derivatives. Not only population growth, but for example when dealing with plagues there can be certain control. An other example can be with diseases, taking all this events together a conclusion can be made.
Differential calculus is a subfield of Calculus that focuses on derivates, which are used to describe rates of change that are not constants. The term ‘differential’ comes from the process known as differentiation, which is the process of finding the derivative of a curve. Differential calculus is a major topic covered in calculus. According to Interactive Mathematics, “We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).” Not only are derivatives used to determine how to maximize or minimize functions, but they are also used in determining how two related variables are changing over time in relation to each other. Eight different differential rules were established in order to assist with finding the derivative of a function. Those rules include chain rule, the differentiation of the sum and difference of equations, the constant rule, the product rule, the quotient rule, and more. In addition to these differential rules, optimization is an application of differential calculus used today to effectively help with efficiency. Also, partial differentiation and implicit differentiation are subgroups of differential calculus that allow derivatives to be taken to more challenging and difficult formulas. The mean value theorem is applied in differential calculus. This rule basically states that there is at least one tangent line that produces the same slope as the slope made by the endpoints found on a closed interval. Differential calculus began to develop due to Sir Isaac Newton’s biggest problem: navigation at sea. Shipwrecks were frequent all due to the captain being unaware of how the Earth, planets, and stars mov...
Ever wonder how scientists figure out how long it takes for the radiation from a nuclear weapon to decay? This dilemma can be solved by calculus, which helps determine the rate of decay of the radioactive material. Calculus can aid people in many everyday situations, such as deciding how much fencing is needed to encompass a designated area. Finding how gravity affects certain objects is how calculus aids people who study Physics. Mechanics find calculus useful to determine rates of flow of fluids in a car. Numerous developments in mathematics by Ancient Greeks to Europeans led to the discovery of integral calculus, which is still expanding. The first mathematicians came from Egypt, where they discovered the rule for the volume of a pyramid and approximation of the area of a circle. Later, Greeks made tremendous discoveries. Archimedes extended the method of inscribed and circumscribed figures by means of heuristic, which are rules that are specific to a given problem and can therefore help guide the search. These arguments involved parallel slices of figures and the laws of the lever, the idea of a surface as made up of lines. Finding areas and volumes of figures by using conic section (a circle, point, hyperbola, etc.) and weighing infinitely thin slices of figures, an idea used in integral calculus today was also a discovery of Archimedes. One of Archimedes's major crucial discoveries for integral calculus was a limit that allows the "slices" of a figure to be infinitely thin. Another Greek, Euclid, developed ideas supporting the theory of calculus, but the logic basis was not sustained since infinity and continuity weren't established yet (Boyer 47). His one mistake in finding a definite integral was that it is not found by the sums of an infinite number of points, lines, or surfaces but by the limit of an infinite sequence (Boyer 47). These early discoveries aided Newton and Leibniz in the development of calculus. In the 17th century, people from all over Europe made numerous mathematics discoveries in the integral calculus field. Johannes Kepler "anticipat(ed) results found… in the integral calculus" (Boyer 109) with his summations. For instance, in his Astronomia nova, he formed a summation similar to integral calculus dealing with sine and cosine. F. B. Cavalieri expanded on Johannes Kepler's work on measuring volumes. Also, he "investigate[d] areas under the curve" ("Calculus (mathematics)") with what he called "indivisible magnitudes.
In society’s current era of technological advancement, video games have gone a long way since they were first created. Video games in the twenty-first century are no longer just toys or junk in the lifestyles of the youth. They have become innovative inventions that not only entertain its users, but also help aid the people in both the academic field and in jobs. The influences that video games bring about in the culture of the youth today are, in fact, not the negative influences that most people think. Video games are actually this generation’s new medium for educating the youth. The information they learn are also mostly positive and useful things that they may apply in their future lives (Prensky 4). In a generation that revolves around technology and connectivity, developers and educators have already been able to produce fun and interesting games that can teach and train people. Video game developers and educators should continue to collaborate in order to create more positive, educational, and appealing games.
Many seem to think of mathematics as being nothing more than a series of numbers and formulas that they must learn, in order to pass a particular requirement for their college degree. They rarely, if ever, stop to think about the importance of mathematics and how it actually affects them and the people around them. It is ...
This evaluation has not only allowed me explore calculus more in depth, but also physics, and the way the world works. This has personally allowed me to explore the connections between math and real-world situations, which is hard to find in textbooks.
When I graduated from high school, forty years ago, I had no idea that mathematics would play such a large role in my future. Like most people learning mathematics, I continue to learn until it became too hard, which made me lose interest. Failure or near failure is one way to put a stop to learning a subject, and leave a lasting impression not worth repeating. Mathematics courses, being compulsory, are designed to cover topics. One by one, the topics need not be important or of immediate use, but altogether or cumulatively, the topics provide or point to a skill, a mastery of mathematics.
...d a better understanding of differentiation, I have had several of my students tell me that I am the best math teacher they have ever had. They express their happiness by telling me that I teach math in a way they understand. They state, “You do not stand in front of the classroom and explain how to do the problem, give us homework, and move on to the next topic”. I take pride in this. I try very hard to help each of my students understand the necessary standards so when they leave my room, they are able to take a real-world problem and find solutions to them.
In my previous studies, I have covered all the four branches of mathematics syllabus and this has made me to develop a strong interest in pure mathematics and most importantly, a very strong interest in calculus.