61. Calculus History The main ideas of calculus developed over a very long period of time. Read about some of the mathematicians who contributed to this field of mathematics. http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_rise_of_calculus.html

A history of the calculus Analysis index History Topics Index Version for printing The main ideas which underpin the calculus developed over a very long period of time indeed. The first steps were taken by Greek mathematicians. To the Greeks numbers were ratios of integers so the number line had "holes" in it. They got round this difficulty by using lengths, areas and volumes in addition to numbers for, to the Greeks, not all lengths were numbers. Zeno of Elea , about 450 BC, gave a number of problems which were based on the infinite. For example he argued that motion is impossible:- If a body moves from A to B then before it reaches B it passes through the mid-point, say B of AB. Now to move to B it must first reach the mid-point B of AB . Continue this argument to see that A must move through an infinite number of distances and so cannot move. Leucippus Democritus and Antiphon all made contributions to the Greek method of exhaustion which was put on a scientific basis by Eudoxus about 370 BC. The method of exhaustion is so called because one thinks of the areas measured expanding so that they account for more and more of the required area.

62. The History Of The Calculus And The Development Of Computer Algebra Systmes Discusses development of integral and derivative calculus from the 17th century. Features contributions by key western civilization mathematicians. Includes examples of selected problems and how they were originally solved in earlier times. Also, covers the historic background to computer algebraic systems. http://www.math.wpi.edu/IQP/BVCalcHist/calctoc.html

The History of the Calculus and the Development of Computer Algebra Systems Introduction History of the Integral from the 17 th Century ... Conclusions A. Bibliography Return to the Main Page

63. Why Study Calculus? A Brief History Of Math Explains, in everyday language, the developments in astronomy, math, and physics that contributed to the discovery of differential calculus and its http://www.math.vanderbilt.edu/~schectex/courses/whystudy.html

Why Do We Study Calculus? or, a brief look at some of the history of mathematics an essay by Eric Schechter version of September 10, 1999 The question I am asked most often is, "why do we study this?" (or its variant, "will this be on the exam?"). Though some students will eventually use integrals and derivatives in their work in physics, chemistry, or economics, most will never use epsilons and deltas. Applied mathematicians may use a theorem such as "the limit of the product is the product of the limits"; we only need epsilons and deltas to prove such theorems. If the applied mathematician takes the attitude that "I trust the pure mathematicians who say they have proved this theorem," then the applied mathematician does not need to study epsilons and deltas at all. But calculus is not a just vocational training course. In part, students should study calculus for the same reasons that they study Darwin, Marx, Voltaire, or Dostoyevsky: These ideas are a basic part of our culture; these ideas have shaped how we perceive the world and how we perceive our place in the world. To understand how that is true of calculus, we must put calculus into a historical perspective; we must contrast the world before calculus with the world after calculus. (Probably we should put more history into our calculus courses. There is a growing movement among mathematics teachers to do precisely that.) The earliest mathematics was perhaps the arithmetic of commerce: If I am willing to trade 3 of my goats for one of your cows, how many goats will 4 cows cost me? The ancient Greeks did a great deal of clever thinking, but very few experiments; this led to some errors. For instance, Aristotle observed that a rock falls faster than a feather, and concluded that heavier objects fall faster than lighter objects. Aristotle's views persisted for centuries, until the discovery of air resistance.

64. Timeline Of Calculus History http://www.mhhe.com/math/calc/smithminton2e/cd/tools/timeline/

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65. Innovative Teaching Exchange: Volumes And History Volumes and history a calculus project using original source reading (a contribution to the Innovative Teaching Exchange series) http://www.maa.org/t_and_l/exchange/ite5/hodgson.html

Volumes and History: A Calculus Project Involving Reading an Original Source Elyn Rykken Mathematical Sciences Department Muhlenberg College Allentown, PA 18104 and Jody Sorensen Department of Mathematics and Statistics Grand Valley State University Allendale, MI 49401 While conducting a survey of old calculus books in the rare book room at American University, we came across James Hodgson's The Doctrine of Fluxions. While the book was originally published in 1726, we looked at a posthumous 1756 edition. We were looking for various calculus books' presentations of volumes of solids of revolution. While Hodgson's notation and language are awkward to our modern eyes, his geometric explanations are clear. Furthermore, he employs a wide variety of techniques that are still taught today. These include the methods using "disks", "washers", and "shells". We decided to use several pages of this text as a reading assignment for our students. What follows is a summary of what we hope to achieve by the project, along with links to the text, including both images of the actual book and our transcribed copy of the pages. We've also included the assignment we give to our students, a summary of the difficulties they have encountered, and their reactions. When teaching our students how to find volumes of solids of revolution, we emphasize visualizing the geometry that is involved. We teach them to consider a representative slice of the region which is to be rotated, and then to imagine what shape this slice will generate when rotated. This naturally leads to the use of disks, washers or shells, depending on the particular slice that is considered. When we discovered Hodgson's treatment of this topic in his text, we were pleased to see that he uses the same approach. We decided that reading this text would be a good exercise for our students. It would reinforce the idea of a representative slice, and it would serve as an introduction to the history of mathematics as a discipline, and to the history of calculus in particular.

66. History Welcome to the history of Math Page. The Babylonian’s mathematics passed on to Newton s Apple The development toward calculus continued with the great http://library.thinkquest.org/4116/History/history.htm

Number problems like the Pythagorean triples (discovered by Pythagoras and the Pythagoreans, his students) were studied from 1700 BC. Linear equations were studied to solve problems, as well as quadratic equations. These led to a kind of numerical algebra. The Greeks studied similar figures, volume and area (geometry problems). Values were also determined for p The ancient Greeks discovered conic sections (circular shapes formed when cutting a cone at different angles). They also made many discoveries in astronomy and trigonometry. Major work in mathematics in Europe began in about the sixteenth century, with the mathematician Girolamo Cardan and some others, such as Tartaglia, Ferrari, and Pacioli. They reformed what people thought the universe and mathematics were like. During the seventeenth century, mathematicians made more and more progress towards calculus and added some algebraic methods to geometry. The development toward calculus continued with the great mathematicians Pierre de Fermat. Together, with Blaise Pascal, they began the mathematical theory of probability. However, calculus evolved in the seventeenth century. Newton, Sir Isaac, discovered the branch of mathematics called calculus. He called it fluxions, which meant changing. His new discoveries contained an interaction between physics, astronomy, and mathematics. His theories on light and gravitation took us to the eighteenth century.

67. The History And Development Of Calculus :: Term Papers, Essays - Free Summary Of A study of the origins of mathematics and the growth of calculus. http://www.academon.com/lib/paper/8857.html

Home Sell Buy FAQs ... Contact Us Welcome to AcaDemon We have thousands of high-quality term papers, research papers, essays, book reports and dissertations on every topic. At AcaDemon, you can download those term papers to help you write yours! You can be sure that the term paper, essay, book report or research paper, you download are top-quality, competitively priced and high-level work. Papers on "The History and Development of Calculus" and similar term paper topics: Paper #008857 :: The History and Development of Calculus - Buy and instantly download this paper now A study of the origins of mathematics and the growth of calculus. 1,825 words, 7 sources, MLA, $ 59.95 USD Paper Summary: 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."

68. Calculus -- Facts, Info, And Encyclopedia Article facts about creative commons) creative commons non commercial license. Carl B. Boyer. (1949) The history of the calculus and its Conceptual Development. http://www.absoluteastronomy.com/encyclopedia/c/ca/calculus.htm

Calculus [Categories: Academic disciplines, Calculus] For other uses of the term calculus see (Click link for more info and facts about calculus (disambiguation)) calculus (disambiguation) Calculus is a central branch of (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics , developed from (The mathematics of generalized arithmetical operations) algebra and (The pure mathematics of points and lines and curves and surfaces) geometry , and built on two major complementary ideas. One concept is called differential calculus . It studies rates of change, which are usually illustrated by the (An elevated geological formation) slope of a line. Differential calculus is based on the problem of finding the instantaneous rate of change of one quantity relative to another. Examples of typical differential calculus problems are finding the following quantities: The acceleration and speed of a free-falling body at a particular moment. The loss in speed and trajectory of a fired projectile, such as an artillery shell or bullet. Change in profitability over time of a growing business at a particular point.

69. Calculus History Books And Articles - Research Calculus History At calculus history Scholarly books and articles on calculus history at Questia, world s largest online library and research service. http://www.questia.com/library/science-and-technology/history-and-philosophy-of-

70. Calculus.org - THE CALCULUS PAGE . Directory of calculus links for tutorials, homework help, history sample tests, and tips on exam preparation. http://www.calculus.org/

calculus.org: THE CALCULUS PAGE Editorial Board Sponsors Prizes and competitions: Results of the 2005 National High School Student Calculus Competition have been finalized. The 2005 winner is Sam Beck. Details can be found at: 2005 Award Calculus.org Resources For The Calculus Student: Calculus problems with step-by-step solutions Calculus problems with detailed, solutions. It's calculus done the old-fashioned way - one problem at a time, one easy-to-follow step at a time, with problems ranging in difficulty from easy to challenging. Also available are scanned solutions to problems in differential integral and multi-variable calculus and series. Excerpts from "How To Ace Calculus" Excerpts from "How to Ace Calculus: The Streetwise Guide" a recently published book with an unorthodox humorous approach to learning calculus. For those with a sense of humor only. Calculus animations in Maple and Calculus animations in Mathematica A series of Quicktime movies, contributed by Deej Heath of Pacific Lutheran University. These illustrate many ideas of calculus, and also include instructions on how to make similar animations yourself using Maple or Mathematica. Calculus Applets A collection of Java applets illustrating calculus concepts by Deej Heath at Pacific Lutheran University.

71. Earliest Uses Of Symbols Of Calculus seems he does not show this symbol in A history of Mathematical Notations.) Judith V. Grabiner, author of The Origins of Cauchy s Rigorous calculus http://members.aol.com/jeff570/calculus.html

Earliest Uses of Symbols of Calculus Last revision: Dec. 1, 2004 Derivative. The symbols dx, dy, and dx/dy were introduced by Gottfried Wilhelm Leibniz (1646-1716) in a manuscript of November 11, 1675 (Cajori vol. 2, page 204). f'(x) for the first derivative, f''(x) for the second derivative, etc., were introduced by Joseph Louis Lagrange (1736-1813). In 1797 in Théorie des fonctions analytiques the symbols f'x and f''x are found; in the Oeuvres, Vol. X , "which purports to be a reprint of the 1806 edition, on p. 15, 17, one finds the corresponding parts given as f(x), f'(x), f''(x), f'''(x) " (Cajori vol. 2, page 207). In 1770 Joseph Louis Lagrange (1736-1813) wrote for in his memoir Nouvelle méthode pour résoudre les équations littérales par le moyen des séries Oeuvres, Vol. III In 1772 Lagrange wrote u' du dx and du u'dx in "Sur une nouvelle espèce de calcul relatif à la différentiation et à l'integration des quantités variables," Nouveaux Memoires de l'Academie royale des Sciences et Belles-Lettres de Berlin Oeuvres, Vol. III

72. From Modernlog@aol.comno-spam (ModernLog) Newsgroups Sci.math A few of the books available on the origin and history of the calculus include Margaret E. Baron, The Origins of the Infinitesimal calculus (NY, Dover, http://www.math.niu.edu/~rusin/known-math/98/calc-hist

From: modernlog@aol.comno-spam (ModernLog) Newsgroups: sci.math Subject: Re: CALCULUS HISTORY Date: 3 Dec 1998 13:28:39 GMT rifurman@aol.com (RIFurman) wrote: >>I am interested in the origin and early history of calculus. Would someone please direct me to some articles or some form of reference, pertaining to this. < Try ant decent university library. A few of the books available on the origin and history of the calculus include: Margaret E. Baron, The Origins of the Infinitesimal Calculus (NY, Dover, 1969) Carl B. Boyer, The History of the Calculus and Its Conceptual Development (NY, Dover, 1959) C. H. Edwards, Jr., The Historical Development of the Calculus (NY/Heidelberg/Berlin, Springer-Verlag, 1979) Judith V. Grabiner, The Origins of Cauchy's Rigorous Calculus (Cambridge, MA/London, MIT Press, 1981)

73. ENC Online: Curriculum Resources: Readings For Calculus (ENC-020288, Complete Re Preface Sources history Background for calculus, by Steven Galovich Episodes from the early history of mathematics, by Asger Aaboe http://www.enc.org/resources/records/full/0,1240,020288,00.shtm

Skip Navigation You Are Here ENC Home Curriculum Resources Search the Site More Options Don't lose access to ENC's web site! Beginning in August, goENC.com will showcase the best of ENC Online combined with useful new tools to save you time. Take action todaypurchase a school subscription through goENC.com Classroom Calendar Digital Dozen ENC Focus ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse Resource of the Day About Curriculum Resources Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. Readings for calculus Series: Resources for Calculus Grades: 12 Post-Sec. ENC#: ENC-020288 Publisher: Mathematical Association of America (MAA) Date: Ordering Information Similar Records Featured in ENC Focus Subjects: Mathematics Calculus. History. Integrated/interdisciplinary approaches Humanities. Resource Type: Professional development; Resource materials for math or science. Media Type: Print material.

74. Calculus And Its History, Fall 2002 Syllabus for HM/MA 004, calculus and its history . Semester I 2002/03 (AS OF 27 November 2002). Instructor, Kim Plofker http://www.brown.edu/Departments/History_Mathematics/HM0004/hm4.html

Readings Assignments Syllabus for HM/MA 004, "Calculus and its History" Semester I 2002/03 (AS OF: 27 November 2002) Instructor Kim Plofker Department History of Mathematics Email Kim_Plofker@Brown.edu Office Wilbour Hall, Room 001 Office phone Office hours W 2:303:30, Th 11:1512:15, 3:305:00 Course Overview: Currently offered as a first-year seminar, "Calculus and its History" is intended for students (whether or not they have already studied calculus) who would like to investigate questions like the following: What is calculus? Who invented it? When and how did it develop? Why is it harder than the math I know already? (In what ways is it easier) What problems inspired its creation? In what ways did its historical setting change its development, and how did its development affect history in general? How did it change the way mathematicians and other people think about mathematical knowledge? Readings of original sources in English translation range from Babylonian mathematical tablets through Euclid and Archimedes, Oresme, Galileo, Leibniz and Newton, to Cauchy, Riemann and Robinson. The course will meet in C hour (MWF 10:0010:50) in Sayles 204 according to the University Calendar from 4 September to 9 December 2002. Assigned texts will consist of books, handouts, and electronic texts containing excerpts from primary sources in English translation, including (but not limited to) the following:

75. The History Of Curvature Throughout the history of mathematics, the analysis of the curvature of curves has Of the two codiscoverers of the calculus, Sir Isaac Newton and http://www.brown.edu/Students/OHJC/hm4/k.htm

The History of Curvature Sometimes nature is too beautiful for words. This is one of the reasons why mathematicians have been so useful over the centuries. While the origins of mathematics lie in mundane processes like counting, the field has been steadily expanding since that time. One of the most significant changes resulting from the growth of mathematics is that it has become less and less focused on the practical and more and more focused on the theoretical. This has been a very slow process, as mathematics is still somewhere between the two extremes. Regardless, this glacier-like revolution has spawned a lot of beautiful mathematics that might not have otherwise come about. One such invention is the study of curvature. Many curves in the plane and in space are simply beautiful. Since words cannot do them justice, mathematicians have developed several ways of describing them. The most common method of describing a curve is to give its parameterization . Another way, however, is to say how much the curve "bends" at each point. This measure of bending is known by the technical word "curvature". It may surprise the reader that curvature is all that is needed to define a curve (up to rigid motions). For example, a curve that has constant curvature must be part or all of a circle (for these are the only curves that have the same amount of bending at every point). The study of this twisting property of curves goes back to ancient times, but few of its goals were realized until the invention of the calculus in the seventeenth century. Throughout the history of mathematics, the analysis of the curvature of curves has been a prime illustration of the beauty of mathematics and an indicator of its progress.

76. Elementary Calculus Course Outline Basic history of this subject may be found here. (long form). For a history of symbols being used in calculus, see this site. http://mathstat.carleton.ca/~amingare/calculus/1notes104.html

NOTES Mathematics 69.104, All Sections. History of Calculus: Point-form history of the Calculus Summary of a history of Calculus. Basic history of this subject may be found here . (long form). For a history of symbols being used in Calculus, see this site Things to remember: The study of Absolute Values in Chapter 1 is crucial for a strong grasp of basic Calculus concepts. You should always strive to work out the Suggested Homework Problems where they appear in the text. Not every continuous function is differentiable...remember K. Weierstrass gave an example of a function (over 100 years ago) which is continuous at every point of the real line but does not have a derivative anywhere! . You can imagine the graph of such a function as having many (infinitely many), spikes or corners. If you want to "understand" this example, look at the book by E.C. Titchmarsh entitled Theory of Functions , Oxford University Press (1930's). These strange nowhere differentiable functions are typical of things caled fractals. Fractals also give rise to examples of nowhere differentiable curves. Websites that exhibit fractals include:

77. Calculus -- From MathWorld Boyer, CB A history of the calculus and Its Conceptual Development. New York Dover, 1989. Courant, R. and John, F. Introduction to calculus and Analysis, http://mathworld.wolfram.com/Calculus.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Calculus and Analysis Calculus General Calculus ... Medical Terminology Calculus In general, "a" calculus is an abstract theory developed in a purely formal way. "The" calculus, more properly called analysis (or real analysis or, in older literature, infinitesimal analysis ) is the branch of mathematics studying the rate of change of quantities (which can be interpreted as slopes of curves) and the length, area , and volume of objects. The calculus is sometimes divided into differential and integral calculus , concerned with derivatives and integrals respectively. While ideas related to calculus had been known for some time ( Archimedes' method of exhaustion was a form of calculus), it was not until the independent work of Newton and Leibniz that the modern elegant tools and ideas of calculus were developed. Even so, many years elapsed until the subject was put on a mathematically rigorous footing by mathematicians such as Weierstrass SEE ALSO: Arc Length Area Calculus of Variations Change of Variables Theorem ... [Pages Linking Here] REFERENCES: Anton, H.

78. History Of The Calculus -- Differential And Integral Calculus Great Inventions calculus. creative commons non commercial license. Carl B. Boyer. (1949) The history of the calculus and its Conceptual Development. http://www.edinformatics.com/inventions_inventors/calculus.htm

EDinformatics Home Today is See the Full List of Great Inventions Calculus Topics in calculus Fundamental theorem Function Limits of functions Continuity ... Lists of integrals Calculus is a central branch of mathematics , developed from algebra and geometry , and built on two major complementary ideas. One concept is differential calculus . It studies rates of change, which are usually illustrated by the slope of a line. Differential calculus is based on the problem of finding the instantaneous rate of change of one quantity relative to another. Examples of typical differential calculus problems are finding the following quantities: The acceleration and speed of a free-falling body at a particular moment. The loss in speed and trajectory of a fired projectile, such as an artillery shell or bullet. Change in profitability over time of a growing business at a particular point. The other key concept is integral calculus . It studies the accumulation of quantities, such as areas under a curve, linear distance travel, or volume displaced. Integral calculus is the mirror image of differential calculus. Examples of integral calculus problems include finding the following quantities: The amount of water pumped by a pump with a set power input but varying conditions of pumping losses and pressure.

79. History Of Computing - Binairy Calculus history of computing. Binary calculus. The binairy arithmatic or calculus was invented by Leibnitz around 1694 and is presumed to be the first one http://www.thocp.net/reference/sciences/mathematics/binairy_calculus.htm

Binary Calculus The binairy arithmatic or calculus was invented by Leibnitz around and is presumed to be the first one working with this idea. One wonders what would have been happend if Leibnitz had worked on it with more enthusiasm and not had fled to the orient to persue other interests. As we all know our counting system is based on the principle of decimal arithmetic. That has not always been the case. We start to count with to 9, a maximum of 10 symbols, inclusive the zero. With these symbols, or digits or ciphers, you can form any number by permutation ( sequence of numbers) of these symbols. It looks a bit overdone to say this here but not every one realizes that this was not the only way to calculate. Fact is that all great mathematicians (Leibnitz, Pascal) are very aware of this in the 17th century this story plays. But most of them find the decimal system the most convenient. Leibnitz has more than fleeting interest in this binary system. Only two digits are used: and 1. Hence the binary (two some) system. And yet it is possible to express any number in binary. This system will later become the basis on which the entire computer industry will be based, not all kind computers as you will read later on but most of them will. It looks a bit overdone to say this here but not every one realizes that this was not the only way to calculate. Fact is that all great mathematicians (Leibnitz

80. The History Of The Calculus And Its Conceptual Development Science and Mathematics Mathematics history of Mathematics pad. Click to enlarge pad The history of the calculus and Its Conceptual Development http://store.doverpublications.com/0486605094.html

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