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Topic: History of calculus

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Calculus

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	History of calculus
		The calculus was widely used, as it was a very powerful mathematical tool, but it was not until the mid-1800s that it was put on a rigorous foundation.
		The calculus of variations may be said to begin with a problem of Johann Bernoulli's (1696).
		The application of the infinitesimal calculus to problems in physics and astronomy was contemporary with the origin of the science.
	www.xasa.com /wiki/en/wikipedia/h/hi/history_of_calculus.html (1324 words)

	Calculus
		Calculus is a branch of mathematics, developed from algebra and geometry, built on two major complementary ideas.
		Leibniz and Newton are usually designated the inventors of calculus, mainly for their discovery of the fundamental theorem of calculus and work on notation.
		Calculus has been extended to differential equations, vector calculus, calculus of variations, complex analysis, time scale calculus, infinitesimal calculus, and differential topology.
	www.math.ucdavis.edu /~temple/MAT21B/SUPPLEMENTARY-ARTICLES/1HistoryOfCalc.html (1866 words)

	BC Education - Calculus 12 - Overview and History of Calculus (Historical Development of Calculus)
		Students gain a better understanding and appreciation for this field of mathematics by studying the lives of principal mathematicians credited for the invention of calculus, including the period in which they lived and the significant mathematical problems they were attempting to solve.
		Conduct a brief initial overview of the historical development of calculus, then deal with specific historical developments when addressing related topics (e.g., the contributions of Fermat and Descares to solving the tangent line problem can be covered when dealing with functions, graphs, and limits).
		Ask students to investigate various mathematicians and the associated periods of calculus development and to present their findings to the class.
	www.bced.gov.bc.ca /irp/math1012/calc12ohch.htm (571 words)

	Reflections on Coursework
		I left with a better understanding of the history of calculus education, and mathematics education in general.
		The research involved in writing the survey of the history of calculus was quite extensive, and answered some of the questions that were brought up in the lab teaching portion.
		After writing a survey of this history of calculus, it was fascinating to actually follow the development of calculus from a different perspective.
	www.duke.edu /~ltr/academic_statement.htm (1115 words)

	AP: Calculus BC
		Calculus BC can be offered by schools that are able to complete all the prerequisites before the course.
		Calculus BC is a full-year course in the calculus of functions of a single variable.
		The content of Calculus BC is designed to qualify the student for placement and credit in a course that is one course beyond that granted for Calculus AB.
	www.collegeboard.com /student/testing/ap/sub_calbc.html?calcbc (401 words)

	Calculus Math Science
		Calculus labs or short quizzes are also included.
		Meant as an introduction to Calculus for nonspecialists, it covers many of the basics including differential equations.
		- Offers calculus application examples for the mathematical properties of a rainbow, the fundamental theorem of calculus, methods of maximizing structural beams in a building, and modeling population growth.
	www.iaswww.com /ODP/Science/Math/Calculus (823 words)

	Open Directory - Science:Math:Calculus
		Calculus is a branch of mathematics concerned with two types of functions: derivatives and integrals.
		Development of calculus ideas began in ancient Greek times starting Archimedes in around 225 BC used the exhaustion method, that was previously developed by Zeno, Eudoxus and others, to prove that the area of a segment of parabola can be derived from knowing the area of circumscribed parallelogram.
		The development of integral and derivative calculus was fairly separate until the 17th century that Barrow, Isaac Newton and Gottfried Leibniz discovered the relationship between the two branches of the field and were able to write a proof for this theorem.
	dmoz.org /Science/Math/Calculus/desc.html (683 words)

	Calculus history
		In fact, although Barrow never explicitly stated the fundamental theorem of the calculus, he was working towards the result and Newton was to continue with this direction and state the Fundamental Theorem of the Calculus explicitly.
		His results on the integral calculus were published in 1684 and 1686 under the name 'calculus summatorius', the name integral calculus was suggested by Jacob Bernoulli in 1690.
		After Newton and Leibniz the development of the calculus was continued by Jacob Bernoulli and Johann Bernoulli.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/The_rise_of_calculus.html (1691 words)

	calculus.org - THE CALCULUS PAGE .
		Calculus demonstrations that you can use in the classroom to spice up your lectures and prevent those nodding heads.
		Single Variable Calculus Mika Seppälä of Florida State University and the University of Helsinki presents classroom type notes on calculus, in pdf and powerpoint format.
		A history of calculus: Part of a math history project at St. Andrews College.
	www.calculus.org (1138 words)

	Why Calculus?
		The foundations of calculus were not secure at the time of invention, and the limitations of calculus were obvious to many critics.
		Calculus is fundamentally a theory of continuous objects.
		The rise of the calculus from the MacTutor History of Mathematics archive at University of St Andrews.
	www.math.nus.edu.sg /aslaksen/teaching/calculus.shtml (1398 words)

	AP: Calculus AB
		Calculus AB is designed to be taught over a full high school academic year.
		However, if students are to be adequately prepared for the Calculus AB examination, most of the year must be devoted to topics in differential and integral calculus.
		In particular, before studying calculus, students must be familiar with the properties of functions, the algebra of functions, and the graphs of functions.
	www.collegeboard.com /student/testing/ap/sub_calab.html (385 words)

	Why study calculus? a brief history of math
		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.
		Its devotees claim that it gives better intuition for calculus, differential equations, and related subjects; it yields the same kinds of insights that Newton and Leibniz originally had in mind.
	www.math.vanderbilt.edu /~schectex/courses/whystudy.html (3210 words)

	History of the Calculus -- Differential and Integral Calculus
		History of the Calculus -- Differential and Integral Calculus
		Newton are usually designated the inventors of calculus, mainly for their separate discoveries of the fundamental theorem of calculus and work on notation.
		Kowa Seki, lived at the same time as Leibniz and Newton and also elaborated some of the fundamental principles of integral calculus, though this was not known in the West at the time, and he had no contact with Western scholars.
	www.edinformatics.com /inventions_inventors/calculus.htm (1543 words)

	BC Education - Calculus 12 - Overview and History of Calculus (Overview of Calculus)
		BC Education - Calculus 12 - Overview and History of Calculus (Overview of Calculus)
		Students will quickly come to realize that calculus is very different from the mathematics they have previously studied.
		Of greatest importance is an understanding that calculus is concerned with change and motion.
	www.bced.gov.bc.ca /irp/math1012/calc12ohco.htm (442 words)

	Calculus - Problems, Activities and Resources
		Calculus is the study of the properties of functions on the real number line.
		Analysis is the study of calculus using a rigorous approach.
		The text, which was developed by the Calculus Consortium based at Harvard, will introduce you to calculus through the study of problems and examples, discussion of theoretical ideas, the use of the calculator, and through applications of the calculus.
	www.math.uic.edu /~hurder/calculus (269 words)

	History of Calculus
		It is considered that the "discovery of calculus" was made in the 16th century; however there has been much debate over who was the first to discovered the concept out of two scientists Sir Isaac Newton and Gottfried Wilhelm Leibniz (left).
		This lead to strong debate throughout Europe as to who discovered calculus as this debate was seen to hamper scientific development in England.
		Leibniz' greatest contribution to calculus was his notation, the controversy between Leibniz and Newton divided English-speaking mathematicians from those in Europe for many years.
	www.bath.ac.uk /~spw20/history.html (400 words)

	BRIEF HISTORY OF VECTOR CALCULUS (Site not responding. Last check: 2007-10-19)
		The need to describe a direction in a plane or in space, combined with the idea of using geometry to approach physical problems (a good example is a parallelogram of forces) brought forth the concept of a vector.
		In the second half of the 19th century, basic concepts and principles that form the foundations of vector calculus were formalized (for example, parallelogram law, which talks about "addition of lines with a direction," formalized a parallelogram of forces).
		The first vector calculus book, E.B. Wilson's Vector Calculus: A Text Book for the Use of Students of Mathematics and Physics Founded upon the Lectures of J.W. Gibbs, published in 1901, was the first book entirely devoted to modern vector calculus.
	www.math.mcmaster.ca /lovric/vcbook/history.html (390 words)

	Calculus history references (Site not responding. Last check: 2007-10-19)
		C B Boyer, The History of the Calculus and Its Conceptual Development (New York, 1959).
		L Pepe, The infinitesimal calculus in Italy at the beginning of the 18th century (Italian), Boll.
		J Vernet, The infinitesimal calculus and Spanish mathematics of the 18th century (Spanish), Arch.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Printref/The_rise_of_calculus.html (497 words)

	Calculus A (Site not responding. Last check: 2007-10-19)
		Calculus A is the first course in a three-course sequence in calculus, primarily intended for students in science and engineering.
		a basic sense of the history of calculus and its central importance in science
		This course is graded A, B, C, D, F. The grade typically depends on a combination of class tests, homework, Maple assignments, quizzes, and a comprehensive final exam.
	www.math.uah.edu /courses/calculus/ma171.html (245 words)

	History of Calculus, Test 1 (Site not responding. Last check: 2007-10-19)
		He was also the first to come up with the "calculus definition" of the tangent line to a curve, and developed methods for drawing them.
		The cycloid is traced about by a point on the rim of a wheel as the wheel rolls along the ground.
		They are used to calculate areas and volumes by comparing a figure of unknown area or volume with one of for which it is known.
	www.math.fau.edu /Richman/HistCalc/test1-ans.htm (393 words)

	History of Calculus
		"Biographical history, as taught in our public schools, is still largely a history of boneheads: ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals -- the flotsam and jetsam of historical currents.
		Though Newton and Leibniz are said to be the inventors of calculus, Fermat certainly had a hand in it.
		It has been said that any elementary or advanced calculus text printed after 1748 is basically a copy or a copy of a copy of Euler.
	www.mathstat.dal.ca /~kgardner/History.html (1654 words)

	Digg - Scholars decode ancient text, shake up pre-calculus history
		On a lark they examined a theretofore unread section of The Method of Mechanical Theorems, which is the book's biggest claim to fame; no other copy of the work is known to exist.
		Considering what was their starting point and how few they actually numbered...the ancient Greeks are almost certainly pound for pound the most influencial thinkers in history.
		In this late text published just five years before his death, Guénon devotes an entire volume to questions regarding the nature of limits and the infinite with respect to the calculus both as a mathematical discipline and as symbolism for the initiatic path.
	digg.com /links/Scholars_decode_ancient_text,_shake_up_pre-calculus_history (1416 words)

	Amazon.com: The History of the Calculus and Its Conceptual Development: Books: Carl B. Boyer (Site not responding. Last check: 2007-10-19)
		Their relevance to calculus is this: the first gave rise to "infinitesimals" (infinitely small quantities); the second to the "limit" or "epsilon-delta" approach.
		The original ideas that began the development of the calculus are very old, the first known exposition of the problems of limits is the well known paradox proposed by Zeno, which dates back to ancient Greece.
		Despite all the genius of Newton and Liebniz, there were still many gaps in the calculus that had to be corrected, which is the subject of the remaining chapters.
	www.amazon.com /History-Calculus-Its-Conceptual-Development/dp/0486605094 (2462 words)

	History of Calculus (Site not responding. Last check: 2007-10-19)
		The beginnings of differentiation were much later, in the work of the early 17th century on tangents to curves and instantaneous rates of change.
		The recognition that these two processes are inverses of each other (the "Fundamental Theorem of Calculus") and the major initial development of the theory occurred in the late 17th century, mainly in the work of Newton (1642-1727) and Leibniz (1646-1716).
		All calculus was based on the concept of a limit, a concept which was not well understood until the 19th century (in the work of Cauchy, Riemann, Weierstrass and others) and until then the results in the calculus were founded on an unsound, non- rigorous basis.
	www.scit.wlv.ac.uk /university/scit/modules/mm2217/hc.htm (167 words)

	SHiPS \|\| The History of Calculus Notation
		Newton developed his infinitesimal calculus between 1664 and 1666 when he was temporarily con-fined to his estate in Woolsthorpe, quarantined from an outbreak of Bubonic plague in England.
		Leibniz originally developed his calculus in order to find methods by which discrete infinitesimal quantities could be summed up to calculate the area of a larger whole.
		When writing of Newton and Leibniz, 20th-century authors of calculus textbooks tend to reduce their history to method and notation while exalting them as insightful, majestic intel-lectual forebears, perpetuating a mathematical mystique that rewards genius and ignores context.
	www1.umn.edu /ships/9-1/calculus.htm (3363 words)

	Scholars decode ancient text, shake up pre-calculus history: 11/02
		Reviel Netz, an assistant professor of classics, might not have actually shouted "Eureka!" on a visit last year to the Walters Art Museum in Baltimore, but that's what he was thinking.
		In the 19th century, mathematicians rebuilt the calculus to create a rigorous and precise "science of infinity," Netz explained.
		People like to simplify forces that shape history, and this can lead to conceptually crude, underdeveloped ideas -- such as that the Victorians were sexually repressed.
	news-service.stanford.edu /news/2002/november6/archimedes-116.html (824 words)

	History Calculus Math Science
		Children can drive parents to early graveHonolulu Advertiser, HI - 11 hours agoThey examined the reproductive history and survival of 21684 couples married between 1860 and 1895.
		Times BulletinHugs and high-fivesTimes Bulletin, OH - Jan 18, 2007"It's an unfathomable notion to think I could possibly be of any help in, say, a calculus or physics class." Kirkendall has substituted in classes in...
		"Calculus is an old problem, but new editions of the same...
	www.iaswww.com /ODP/Science/Math/Calculus/History (350 words)

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