| Papers [1-14] of 22 :: [Page 1 of 2] | | Go to page : 1 2 —> | Search results on "CALCULUS": |
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Calculus, 2006.
An overview of the mathematical concept of calculus.
1,713 words (approx. 6.9 pages), 12 sources, MLA, £ 28.95
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Abstract
Calculus is divided into two branches, one being differential and the other being integral. This paper provides an overview of calculus and examines the two branches in more detail. It also looks at the importance of calculus in the world today.
From the Paper
"It must be stated that Newton's mathematics that involved 'fluxions' was one of the first forms of the area defined as 'differential calculus'. Although Newton used and preferred to use geometrical methods to algebraic equations, calculus methods had come into importance. However, calculus was not widely accepted at the time, and there were several philosophical objections to the science, but the fact remains that these objections over the years have made no difference to the application of the science."
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The History and Development of Calculus, 2002.
A study of the origins of mathematics and the growth of calculus.
1,825 words (approx. 7.3 pages), 7 sources, MLA, £ 30.95
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Abstract
This paper presents a detailed examination of the history of calculus. The writer takes the reader on an exploratory path through the origins of mathematics and then on to the history of calculus. The people who are credited with its invention as well as the forms that it took are all included in the discussion.
From the Paper
"The history of mathematics is one in which the topic follows the actual subject. Mathematics are taught by building on foundational blocks. Each block is taught and mastered and when that is completed the next block is introduced. The origin and history of mathematics follows the same path. The history of calculus is perhaps the most interesting of the mathematical techniques. The history and origin of calculus is founded in philosophy as well as science and it is one of the most fascinating of the mathematical theories and practices."
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High School Calculus, 2006.
A review of the literature 'Understanding the Concepts of Limit and Continuity in Calculus Courses at the High School and/or Early College Level'.
4,037 words (approx. 16.1 pages), 13 sources, MLA, £ 57.95
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Abstract
This paper reviews and discusses the literature 'Understanding the Concepts of Limit and Continuity in Calculus Courses at the High School and/or Early College Level'. According to the paper, the ten fastest growing career fields include five that are computer-related which rely heavily on the knowledge of mathematics.
Outline:
Background and Overview
Studies in the Concept of Limit and Continuity in High School and Early College-Level Calculus Courses
Interactions of Methods and Questions for Further Study
From the Paper
"Clearly, then, just going through the motions and mechanics of calculus may serve to help familiarize these young learners with the basic steps involved. There are a number of studies to date, though, that have confirmed that these students typically experience a number of problems in understanding key calculus concepts that adversely affect their ability to master them (Bezuidenhout, 2001). To help facilitate the process, just as handheld calculators have been introduced into some early mathematics classes to facilitate routine calculations to allow more time for instruction, Heid (1988) suggested early on that computers could likewise be used to help beginning calculus students learn more by automating the algorithmic functions required. Although there is clearly a trade-off involved in such an approach, this author maintains that this approach would allow more class time for development of higher mathematics concepts."
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Calculus and its Application to Aerodynamics, 2002.
This paper explores some of the different applications of calculus to the field of aerodynamics.
2,525 words (approx. 10.1 pages), 5 sources, APA, £ 39.95
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Abstract
This paper states that the field of aerodynamics could not exist without calculus. The author discusses the most prevalent and widely used equations. The advent of the computer has greatly improved the use of these equations in the field and allowed the field of aerodynamics to become more precise.
Table of Contents
Introduction
The Myth about Bumblebee Flight
Turbulence
The Bermouli Equation
Continuity Equation
Navier-Stokes Equations
Conclusion
From the Paper
"Math is the language of science. The different disciplines of math relate to different areas of science. Science needs math in order to be understood. Algebra allows us to create sentences using numbers to describe an event. Geometry and Trigonometry help us to describe shapes, and Calculus is the tool for describing change. It can be a change in angles as in vector calculus, a change in rate, a change in speed, or almost any other change."
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"The History of Calculus" by Carl B. Boyer, 1991.
This paper reviews "The History of Calculus" by Carl B. Boyer, the evolution and philosophy of this mathematical discipline.
2,925 words (approx. 11.7 pages), 1 source, £ 54.95
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From the Paper
"The purpose of this research is to examine "The History of Calculus" by Carl B. Boyer. The plan of the research will be to set forth the general ideas in the book, and then to explore details contained in the book that summarize the concepts of calculus that Boyer wants to emphasize.
Boyer's The History of the Calculus is put forward as one of the few histories of how the discipline of calculus evolved, apart from an explanation of how to use it mathematically. It is by positioning the ideas of mathematics and philosophy that influenced calculus that Boyer gradually moves toward an explanation of how calculus can actually be used and applied. The background of Boyer's approach appears to be the idea that a richer understanding of how calculus came to "be" in the world of ideas can lead to an understanding of how it can be employed in ... "
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The Impact of Newtonian Science, 2002.
A description of Newton's creation of calculus and its impact on the world, both socially and scientifically.
1,825 words (approx. 7.3 pages), 8 sources, MLA, £ 30.95
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Abstract
This paper helps to explain and justify the creation of calculus. Isaac Newton helped to solve some of the most perplexing problems the world has imagined, and the method he used in doing so is still used for the same purpose today. Newton's creation of calculus and ideas of using it to prove the universal laws of nature made human reason the most powerful method of thought and most definite route to seeking the truth.
From the Paper
"In mathematics, a certain surprising thing happens again and again. Someone poses a simple question, a question so simple that it seems no useful result can come from answering it. And yet it turns out that the answer opens the door to all kinds of interesting developments, and gives great power to the person who understands it." (Saywer 3) This quote from a prestigious professor of mathematics parallels the story of Isaac Newton and his development of calculus. Isaac Newton helped to solve some of the most perplexing problems the world has imagined, and the method he used in doing so is still used for the same purpose today. There is a popular myth that Newton was sitting under a tree when an apple fell from it, and he asked himself what force could pull the apple to the Earth. Whether this story is true or not is uncertain, but the image is clear of Newton getting hit on the head with the apple of epiphany. He used calculus to prove that gravity pulled objects to Earth and held the planets together, and also to prove his world-renowned three laws of motion. By forming this revolutionary method of problem solving, Newton not only paved the way for new roads in mathematics but also changed the way that people thought and sought out answers. Newton's creation of calculus and ideas of using it to prove the universal laws of nature made human reason the most powerful method of thought and most definite route to seeking the truth.
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The Newtonian Universe, 2004.
This paper studies the Newtonian Universe, laws of gravity, the development of calculus, the laws of motion and the idea of the clockwork universe.
1,582 words (approx. 6.3 pages), 4 sources, MLA, £ 28.95
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Abstract
This paper looks at the Newtonian Universe, laws of gravity, the development of calculus, the laws of motion and the idea of the clockwork universe.
From the Paper
"Sir Isaac Newton was considered by many the most important figure in the development of modern science, and his accomplishments covered a broad scope, from fundamental contributions to physics and astronomy, to the invention in parallel with Liebnitz of the mathematical field of calculus and Newtonian mechanics which came to be regarded as the ultimate explanatory science. Sir Isaac Newton changed the understanding of the universe with his three laws of motion."
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Evolution of Mathematics, 1993.
Ancient Greece to 1990s. Major figures & discoveries of mathematics. Looks at principles, calculus, physics, specialization and algebra. Compares the attitude differences between U.S and Japan.
3,600 words (approx. 14.4 pages), 16 sources, £ 66.95
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From the Paper
" The Evolution of Mathematics:
The American and Japanese Perspectives
Elementary forms of mathematics have probably been with man throughout his evolution. As human societies advanced, so too did mathematics. From the 1500s to the present, a long lineage of mathematicians have revolutionized the field. These men were often of European origin. Only in the last century has the United States and Japan emerged as dominant mathematical forces. At present, either of these nations could lead the field into the future.
The first systems of numeration were invented by the Greeks and the Romans (Struik, 1987, p. 80.81). Later, the Western merchant, Leonardo of Pisa, introduced the Hindu.Arabic system of numeration into Western Europe. Europeans came to accept these.."
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Guillaume Francois Antoine de L'Hopital, 2005.
This paper discusses mathematician Guillaume Francois Antoine de L'Hopital, born in Paris, France in 1661.
1,445 words (approx. 5.8 pages), 7 sources, MLA, £ 24.95
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Abstract
This paper explains that L'Hopital, who lived during the conception of modern calculus, was taught by Bernoulli; the result of this tuition was L'Hopital's "Analyse des Infiniments Petits", which became the French reference book in the calculus for a century. The author points out that L'Hopital's name is guaranteed to survive in the memories of thousands of mathematicians because of the L'Hopital rule, which is useful when dealing with indeterminate forms. The paper relates that L'Hopital created the template by which all calculus texts would be modeled and measured against for the next three hundred years. Formulas included.
From the Paper
"A natural progression from his two first works on the topic of calculus would have been a serious examination of the integral calculus. Indeed, this was a project that L'Hopital was capable of and actually began to write before his death. However, one of his contemporaries-Leibniz-made it known to L'Hopital that he also endeavored to publish a work covering the same hole in written calculus of the time. Apparently, out of respect to the mathematician who made much of his fame possible, L'Hopital abandoned the project."
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Stepran's Infinity Puzzle, 2008.
This paper discuses Stepran's infinity puzzle as an excellent method to explore the character of infinity relative to tangible outcomes.
1,625 words (approx. 6.5 pages), 3 sources, MLA, £ 27.95
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Abstract
This paper explains that the solution to Stepran's infinity puzzle
is not so difficult and has nothing to do with infinity, although the calculus of this equation may in fact be infinite. The author underscores that the puzzle is not a puzzle at all and is not indicative of infinity but rather is purely an exercise in the limitations of physics. The paper agrees with Rucker's concept of infinity as simply a natural element of the universe or of being one of the basic functional elements of mathematical device. The author concludes that the useful concept of infinity is that it does naturally occupy points in both physical and mathematical space ,which truly cements it within the context of a tangible mathematical and physics principle rather than some far-off rationale construct created and identifiable only by mathematical theorists.
Table of Contents:
The Puzzle
The Solution
Response Page to Postings
Discussion
From the Paper
"Stepran's states that a person is tasked with turning a light switch off and on starting with on at 2 minutes and then in increments by half of the time remaining flipping the switch to the opposite position. On the surface the outcome appears as if it will be a simple persuasion of the ineluctable quality of time; that, time is unavoidable and all things must come to an end. Yet, as one begins the calculations it becomes apparent that the half increments are, apparently, infinite starting with two in terms of seconds: 120, 60, 30, 15, 7.5, 3.75, 1.875, .93, .46, .23, .117, .058, .029, ad infinitum, at least to the extent that a common calculator is capable of dividing."
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Mathematician Daniel Bernoulli, 2005.
This paper discusses the life and achievements of mathematician Daniel Bernoulli.
1,995 words (approx. 8.0 pages), 6 sources, MLA, £ 33.95
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Abstract
This paper explains that Daniel Bernoulli used his analytical skills across a broad range of scientific disciplines including probability, hydrodynamics, the flow of blood and blood pressure and Riccati's differential equations. The author points out that Daniel Bernoulli improved mathematical physics with his recognition of many of Newton's theories and his utilization of the more powerful calculus of Leibniz. The paper relates that Bernoulli's mathematical explanation of the behavior of gas led to Boyle's law.
Table of Contents
Introduction
Bernoulli's Contributions to Mathematics
Effect of Bernoulli's Work on Today's World
From the Paper
"Aerodynamics is a subdivision of fluid mechanics that deals with the motion of air and other gaseous fluids, and with the forces acting on bodies in motion relative to such fluids. Some of the examples of aerodynamic actions are: the movement of an aircraft through the air, the wind forces applied on a structure and the working of a windmill. Daniel Bernoulli's principle is the main law dictating the motion of fluids, which links an increase in flow velocity to a decrease in pressure. For instance, for the same quantity of air at the entry to the venturi tube below to flow through the restriction in the middle, the air must accelerate."
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Higher Mathematics, 2007.
An extensive study on the importance of a solid higher mathematics foundation.
7,233 words (approx. 28.9 pages), 15 sources, MLA, £ 83.95
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Abstract
This paper recognizes the the growing importance of higher mathematics for young people today. The paper explains its use in the modern technological arena. It claims that there have been a number of studies in recent years that have focused on how to best communicate the concepts of limit and continuity in higher mathematics. The author explores how to help young learners make the leap of intellect required to master these concepts. The paper uses schematic representation to qualify points made.
Table of Contents:
Background and Overview
Studies in the Concept of Limit and Continuity in High School and Early College-Level Calculus Courses
Interactions of Methods and Questions for Further Study.
Real-World Applications of Limit and Continuity Theory.
References
From the Paper
"Clearly, then, helping high school and early college students achieve mastery of complex subject matter such as calculus frequently requires more than a cursory understanding of how young learners acquire and retain knowledge and what processes serve to facilitate this acquisition and retention. For instance, in their study, "Conceptual knowledge of introductory calculus," White and Mitchelmore (1996) point out that, "Research into the understanding of calculus has shown a whole spectrum of concepts that cause problems for students. In particular, student difficulties with the abstract concepts of rate of change and function are well documented. These concepts involve mathematical objects or processes specific to calculus. Another aspect that needs to be considered is the question of what other concepts are involved in applying calculus knowledge" (p. 79)."
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Johnson & Johnson: Social Responsibility, 2007.
Examines how the Johnson & Johnson company can be considered a model of corporate social responsibility.
6,050 words (approx. 24.2 pages), 15 sources, MLA, £ 74.95
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Abstract
This paper argues that Johnson & Johnson is a prime example of a company directed by "virtue ethics." As evidenced by the Tylenol crises, J&J executives do not resort to a moral calculus (Utilitarianism) or a deontological (rule-based) method of ethical decision making (Kant). The paper evaluates the company in terms of corporate control devices, stakeholder theory, the CSR pyramid, Kohlberg's theory of moral development and ethical theory.
Outline:
Introduction
Company History
The Tylenol Crisis
The Evaluation
References
From the Paper
"When all was said and done the recall of Tylenol* alone cost Johnson & Johnson over $100 million. Prior to the crisis, Tylenol held a 37% market share, outselling its four nearest competitors combined. Within weeks after the crisis its market share had dropped to 7%. When asked about the future of Tylenol, Madison Avenue guru Jerry Della Femina told a New York Times reporter "I don't think they (J&J) can ever sell another product under that name.""
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