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."

Tags:Karl, Popper, science, Isaac, Newton, Thales

Abstract
In considering the great controversy as to who discovered the calculus, either Newton or Leibniz, this essay argues that the accolade should go to Newton. The decision is made on the ground as to who conducted himself most honorably in the affair. There is no doubt that both scientists come to independent discovery and formulation of the calculus. The essay is at pains to point out the greatness of Leibniz, as philosopher, scientist and mathematician. It even acknowledges that Leibniz's formulation of the calculus is superior, and that this superiority derives from his related philosophy of monadology. But Leibniz certainly acts suspiciously during the controversy. The writer maintains that in contrast, Newton at all times displays magnanimity and selflessness. The writer concludes that Newton does not need accolades for his contributions to shine, and yet they shine on their own merits.

From the Paper
"Calculus to Newton was merely a tool that he required to come to his universal theory of gravitation and motion, and not something that should be flouted separately. He was even reluctant to publish the revolutionary Principia, and did so only after the prodding of Edmund Halley.
"Leibniz, on the other hand, was eager to publish and propagate his findings. While we admit to his originality to a large extent, the conduct of Leibniz is highly suspicious in the proceedings. He makes no defense of his integrity, as Newton does, but instead seem entirely intent on pushing the evidence alone, as if defending himself in a court of law, and this makes us feel that he is hiding something. Subsequent scholarship does indeed reveal that he manipulated documents before being released."

Tags:monadology, fluxions, continental, debate

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."

Tags:mathematics, student, ability, geometrically, physics, concept, application

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."

Tags:math, philosophy, theories, practices, application, infinity, infinitesimals, optimization, central, limit, theorem

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."

Tags:math, science, computer, simulation, bumblebee, myth, turbulence, vector, transitional, flows, reynolds, airplane, velocity, field, navier-stokes, equation, bermouli, wing, magnus, stagnation, streamline, dynamic, pressure, continuity, equation, physics, mass, dynamic, pressure, de

Abstract
The paper explains that a linear transformation (also called a linear map or a linear operator) is defined as a function between two vector spaces, one that preserves the operations of vector addition and scalar multiplication. The paper discusses how linear transformations are often used to simplify problems and relates that the term "linear" refers to the form of the equations involved.

From the Paper
"A linear transformation (also called a linear map or a linear operator) is defined as a function between two vector spaces, one that preserves the operations of vector addition and scalar multiplication. Linear transformations are often used to simplify problems, such as finding the natural axes for conic sections, using Ax^2 + 2Hxy + Cy^2 = K. The term "linear" refers to the form of the equations involved--in two dimensions, + = . Geometrically, this represents a line, but if the variables are replaced by vectors, functions, or derivatives, the equation then becomes a linear transformation. When using a system of equations of this sort, one is using a system of linear transformations."

Tags:linear, algebra, geometry

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 ... "

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.

Tags:calculus, impact, Newton, physics, social, mathematics, Isaac, apple, problem, solving

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."

Tags:gravity, clockwork universe, calculus, laws of motion

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.."