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Isaac newton major contributions to math
Essay on how issac newton discovered calculus
Isaac newton major contributions to math
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What is Calculus?
A definition found of calculus in a dictionary was this; a method of computation or calculation in a special notation (as of logic or symbolic logic). The historical perspective of calculus is that people had a problem in finding areas and finding tangent lines. The thing that was discovered to figure these problems out was calculus. Some influential people in the development of calculus were Isaac Newton (1642-1727), and Gottfried Wilhelm Leibniz (1646-1716). Isaac Newton is considered on of the most influential men in the development of calculus. Newton at first kept all his discoveries to himself. He feared that people would not accept his work and disagree with them. He wrote one of the most important scientific books of all time, Philosophiae Naturalis Principia Mathematica. It took the work of another man to finally convince him to publish his work on calculus, Gottfried Wilhelm Leibniz. Leibniz is another influential man in the history of calculus. He taught himself mathematics. Leibniz accomplished what Newton did, but was not recognized for his work as much as Newton was.
Calculus is important in my major of Biomedical engineering because there are many machines that are made possible for humans benefit. MRI (magnetic resonance imaging) is made possible for looking at internal tissues of the human body. Another example would be controlling chaotic behavior in the human heart. I think that calculus will be very helpful in my major, so it is important for me to understand it as best as I can.
I think that the class is going at a fast pace. I have to study a lot to keep up. It seems that lately I understand it, but on the last exam I made stupid mistakes. I need to get more practice done. I like the way you make us read the up coming sections. I get a better feel of what is being covered in class.
I find limits to be interesting to me. I sort of understood them, but I still have some problems in grasping the idea.
...use many of his concepts and ideas today, such as the law of conservation of matter and the calculus concept of dy/dx. Leibniz sought after knowledge and gave the world many new and innovative ways to think. Through his advancements in mathematics, many other fields of study took root and thrived. Leibniz died November 14, 1716. His contributions to society brought about a new way of thinking and challenged what the world knew.
This class was far more intense than what I expected but I was able to make it through the semester. I learned a lot from this class that I will carry into the future and use in other classes. All of the revision and feedback I have received during the time in the class helped me in the end. I feel like I am gradually becoming a better writer. I will take everything that I have learned in this class and use it for future reference when writing papers. I overall have enjoyed this class this semester.
When looking at not just this class but all of my classes and looking at how I have been approaching them versus how I should approach them it definitely puts my mind in a different perspective because I am a person that “strives for excellence” and if I am able to “ace” a class then I definitely try and do that but a lot of the time that doesn’t mean sitting there and actually learning the information it means
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 argument in this paper that even though the onus of the discovery of calculus lies with Isaac Newton, the credit goes to Leibniz for the simple fact that he was the one who published his works first. Appending to this is the fact that the calculus wars that ensue was merely and egotistic battle between humans succumbing to their bare primal instincts. To commence, a brief historical explanation must be given about both individuals prior to stating their cases.
Gottfried Wilhelm Leibniz is an important figure in the history of philosophy and mathematics. Although his work was not fully appreciated during his day, he did much to advance the "thinking" on a variety of subjects. His fame was scarred by the infamous controversy with Isaac Newton on the subject of the discoverer of calculus. Leibniz's work encompassed a wide scope, ranging from philosopy to politics to mechanics and mathematics, but his most noteworthy accomplishment was the discovery of differential calculus and its highly efficient notation.
Isaac Newton invented Calculus to explain gravity and physics. Using his formula, he discovered that planets did not orbit the sun circularly, but elliptically. Through his discoveries, Newton proved that the secrets of the natural world could be known through observation. Newton is known for his mechanistic cosmology. He attributed the creation of the cosmos to God, but God would only come back when the machine was broken.
You cannot talk about the history of mathematics, without mentioning the honorable Sir Isaac Newton. Perhaps one the greatest scientists of the past, Newton has made significant contributions to the fields of mechanics, optics, and mathematics. Before becoming one of the greatest minds of the 18th century, there were some challenges to Newton’s life.
It was through extended communication with Gottfried Leibnitz that Bernoulli was exposed to calculus. When he returned from his travels to Basel in 1682, he founded a school of mathematics and the sciences, and married his wife Judith Stupanus two years later. He became Professor of Mathematics at the University of Basel in 1687, which he retained for the rest of his life, and also began tutoring his brother in calculus. At the time, Leibnitz’s work was not very well known among mathematicians, and the Bernoullis were among the first to try to understand and apply Leibnitz’s discoveries.
This paper presents a development of mathematical analysis, illustrating the contribution of Euler to the development of calculus in the specific examples. Mathematical analysis is a combination of divisions of mathematics that includes differentiation, integration, limits, infinite series and analytic function. First ideas of the concepts of mathematical analysis were established by the ancient Greek mathematicians. All the divisions of calculus, including analysis, had a similar idea: division on the infinitely small elements but the nature of analysis was unfamiliar to the authors of an idea. They developed the principle of infinity and established a method to calculate the area and volume of some plane figures and solids.
The population of the world is growing extremely fast. Eventually there is going to be overpopulation and resources are going to run out if something is not done. We know earth is overpopulated and that a control over population can be made or at least something can be done so there is not a catastrophe. Population growth can be determined using exponentials which directly relate to derivatives. This is a tool that can be very helpful for anthropologist and sociologists in the world (which have nothing to do with mathematics). Not only to know population numbers in ten or twenty years but to have control over other things. For example will there be enough food for five billion people in the world, will there be enough mineral supply for five billion people in the world or will there be enough fuel supply for five billion people in the world. Many of those types of investigations can be determined with the application of derivatives.
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.
...ocity. On the other hand, Leibniz had taken a geometrical approach, basing his discoveries on the work of previous thinkers like Fermat and Pascal. Though Newton had been the first to derive calculus as a mathematical approach, Leibniz was the first one to widely disseminate the concept throughout Europe. This was perhaps the most conclusive evidence that Newton and Leibniz were both independent developers of calculus. Newton’s timeline displays more evidence of inventing calculus because of his refusal to use theories or concepts to prove his answers, while Leibniz furthered other mathematician’s ideas to collaborate and bring together theorems for the application of calculus. The history of calculus developed as a result of sequential events, including many inventions and innovations, which led to forward thinking in the development of the mathematical system.
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.
The subject grew into what is now known as differential and integral calculus (Westfall, 1993).Based on his earlier work in fluxions, was development of calculus. “One of the greatest contributions to modern mathematics, science, and engineering was the invention of calculus near the end of the 17th century,” says The New Book of Popular Science (Grolier, 2000). Without the invention of calculus, many technological accomplishments, such as landing on the moon, would have very been difficult.