21. Simon Harding : History Of Calculus Calculus Today. Today calculus is taught in high schools and universitiesacross the world. With the aid of computers we can solve http://www.maths.adelaide.edu.au/people/pscott/history/simon/calculus7.htm

Calculus Today Today calculus is taught in high schools and universities across the world. With the aid of computers we can solve problems previously unsolvable, and with complicated numerical approximations, we can generate useful solutions for problems that otherwise could not be reached. But the fundamentals are still the same. Integration a b ). The area under the curve lies between the lower sum (shown in red, always less than the actual area) and the upper sum (in blue, always greater), and is approximated ever more closely by these sums as the number ( n ) approaches infinity. Differentiation Differentiation is usually described as finding slopes of tangents, and is best described geometrically. Given two points on a curve, the slope of the chord that joins then is close to the slope of the curve. If we consider the effect of moving the two points closer together we see that the slope of the chord approached that of the curve. Home Archimedes Calculus Takes Form Newton ... Calculus Today

22. History Of Calculus The History of the Calculus and the Development of Computer Algebra Systems.Dan Ginsburg Brian Groose Josh Taylor Prof. Bogdan Vernescu, Advisor. http://www.math.wpi.edu/IQP/BVCalcHist/

The History of the Calculus and the Development of Computer Algebra Systems Dan Ginsburg Brian Groose Josh Taylor Prof. Bogdan Vernescu, Advisor An Interactive Qualifying Project @ WPI Abstract A technical examination of the Calculus from two directions: how the past has led to present methodologies and how present methodology has automated the methods from the past. Presented is a discussion of the mathematics and people responsible for inventing the Calculus and an introduction to the inner workings of Computer Algebra Systems. The Paper The Symbolic Calculator

23. BC Education - Calculus 12 - Overview And History Of Calculus (Historical Develo Calculus 12 Overview and history of calculus (Historical Developmentof Calculus). This sub-organizer contains the following sections http://www.bced.gov.bc.ca/irp/math1012/calc12ohch.htm

Calculus 12 - Overview and History of Calculus (Historical Development of Calculus) This sub-organizer contains the following sections: Prescribed Learning Outcomes Suggested Instructional Strategies Suggested Assessment Strategies Recommended Learning Resources PRESCRIBED LEARNING OUTCOMES It is expected that students will understand the historical background and problems that lead to the development of calculus. It is expected that students will: describe the contributions made by various mathematicians and philosophers to the development of calculus, including: Archimedes Fermat Descartes Barrow Newton Leibniz Jakob and Johann Bernoulli Euler L’Hopital SUGGESTED INSTRUCTIONAL STRATEGIES 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). For additional ideas, see the suggested instructional strategies for other organizers.

24. Oresme, Nicole Concise biography with a note on his mathematical contributions. http://occawlonline.pearsoned.com/bookbind/pubbooks/thomas_awl/chapter1/medialib

Oresme, Nicole (ca. 13201382) Frenchman Oresme went to the University of Paris in the 1340s, studying theology and liberal arts. Later he was a faculty member and administrator at the same university. Oresme served royalty as an educator and a scholar and, therefore, had support for his research. He translated Aristotle into French. Eventually he was made a bishop. He began to think about mathematics and in particular rates of change, like velocity and acceleration. His work entitled De configurationibus (1350s) contained results in geometry and was the first to present graphs of velocities. The argument we use to show the divergence of the harmonic series was devised by Oresme in this publication. Oresme was a popularizer of science and did not believe in Albert of Saxony’s generally accepted model of free fall. Oresme preferred Aristotle’s constant-acceleration model, which became popular among Oxford scholars in the 1330s and was eventually refined and tested by Galileo three hundred years later. In another publication

25. BC Education - Calculus 12 - Overview And History Of Calculus (Overview Of Calcu Calculus 12 Overview and history of calculus (Overview of Calculus).This sub-organizer contains the following sections Prescribed http://www.bced.gov.bc.ca/irp/math1012/calc12ohco.htm

Calculus 12 - Overview and History of Calculus (Overview of Calculus) This sub-organizer contains the following sections: Prescribed Learning Outcomes Suggested Instructional Strategies Suggested Assessment Strategies Recommended Learning Resources PRESCRIBED LEARNING OUTCOMES It is expected that students will understand that calculus was developed to help model dynamic situations. It is expected that students will: distinguish between static situations and dynamic situations identify the two classical problems that were solved by the discovery of calculus: the tangent problem the area problem describe the two main branches of calculus: differential calculus integral calculus understand the limit process and that calculus centers around this concept SUGGESTED INSTRUCTIONAL STRATEGIES 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. It is a mathematics of change that enables scientists, engineers, economists, and many others to model real-life, dynamic situations. The concepts of average and instantaneous velocity are a good place to start. These concepts could be related to the motion of a car. Ask students if the displacement of the car is given by

26. Body Math 403 Spring 2003 Questions from Students related to the history of calculus.Summary of Calculus Questions. We will try to answer them during the semester. http://www.math.cornell.edu/~henderson/courses/M403-S03/calc-questions.htm

Math 403 - Spring 2003 Questions from Students related to the History of Calculus Summary of Calculus Questions We will try to answer them during the semester. Motivation for developing calculus: How and why did integrals and derivatives originate? Where did derivatives come from? How did they figure out the relationship between distance, speed, and acceleration? Calculus is used in many different areas. It seems to me that two primary uses are different in nature. One is its use in geometry as far as finding areas and volumes; the second is its uses in physics, the most basic being the relationship between acceleration, speed and location. What was the motivation for the creation of Calculus? How and why was calculus first thought of and how is it used in today's world? How it developed vs. how it looks today: How did the development of calculus differ from the way we learned it in high school? How does one invent calculus? Was it very much like the way it is now? What prompted the investigation of the idea of imaginary numbers and square roots? Other questions about the development of calculus: In what order did important concepts in calculus develop? (limits, series, derivatives, integrals) Did they each develop in one place/time or can they be credited to different people/places?

27. The History Of Calculus Discusses the development of analyticgeometry, derivative and integral functions dating from Archimedes to Newton....... Name The history of calculus http://www.science-search.org/index/Math/Calculus/6370.htm

Search in Science-Search.org for: What's new Top Searches Statistics Science News ... Home : Detailed Information Name: The History Of Calculus Description: Discusses the development of analytic geometry, derivative and integral functions dating from Archimedes to Newton. Category: Calculus Url: http://www.nd.edu/~hahn/ Date: Current Rating: Clicks/Hits Received: Rate this web site: Rating: Votes: Web site owner: Allow people to rate your site on your site Modify your link Something wrong with this resource? Report this link as broken About Us Contact Us Site Guide ... Add Science Search to Your Web Site The Science Search Directory is based on DMOZ. Science Search has modified and enhanced this data. Submitting to DMOZ: Help build the largest human-edited directory on the web. Submit a Site Open Directory Project Become an Editor Science Search's Sponsors: Goom NL

28. "The History Of Calculus" By Carl B. Boyer:: Term Papers And Essays :: Free Summ The history of calculus by Carl B. Boyer. Abstract. From The Paper. The purposeof this research is to examine The history of calculus by Carl B. Boyer. http://www.academon.com/lib/paper/18658.html

Free Summary of Paper #18658 BUY THIS PAPER LOOK FOR MORE RESEARCH PAPERS, ESSAYS AND BOOK REPORTS "The History of Calculus" by Carl B. Boyer This paper reviews "The History of Calculus" by Carl B. Boyer, the evolution and philosophy of this mathematical discipline. Paper #: # of words: # of sources: Written: Author: Research Author's background: We have been writing papers, reports, and essays for over 30 years. Our staff is composed of professional writers who write academic research for a living. You can count on our quality and experience. Abstract 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 ... " Related Searches Term papers on "The History of Calculus" by Carl B. Boyer

29. The History And Development Of Calculus:: Term Papers And Essays :: Free Summary This paper presents a detailed examination of the history of calculus. The historyof calculus is perhaps the most interesting of the mathematical techniques. http://www.academon.com/lib/paper/8857.html

Free Summary of Paper #8857 BUY THIS PAPER LOOK FOR MORE RESEARCH PAPERS, ESSAYS AND BOOK REPORTS The History and Development of Calculus A study of the origins of mathematics and the growth of calculus. Paper #: # of words: # of sources: Format: MLA Written: Author: 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." Keywords MATH PHILOSOPHY THEORIES PRACTICES APPLICATION INFINITY INFINITESIMALS OPTIMIZATION CENTRAL LIMIT THEOREM Related Searches Term papers on The History and Development of Calculus Essays on The History and Development of Calculus Research papers on The History and Development of Calculus Student papers on The History and Development of Calculus Book reports on The History and Development of Calculus

30. History Of Calculus history of calculus. http//www.maths.adelaide.edu.au/people/pscott/history/simon/calculus1.htm.http//hilbert.dartmouth.edu/~m1f01/history.htm. http://www.math.uiowa.edu/~vshimano/Calc1/history.html

History of Calculus http://www.maths.adelaide.edu.au/people/pscott/history/simon/calculus1.htm http://hilbert.dartmouth.edu/~m1f01/history.htm http://occawlonline.pearsoned.com/bookbind/pubbooks/thomas_awl/chapter1/medialib/custom3/timeline.htm http://www.nd.edu/~hahn ... http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/The_rise_of_calculus.html

31. From Modernlog@aol.comno-spam (ModernLog) Newsgroups Sci.math Subject Re CALCULUS HISTORY Date 3 Dec 1998 132839 GMT rifurman@aol.com (RIFurman)wrote I am interested in the origin and early history of calculus. 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)

32. Calculus Resources For Math Educators Isaac Newton. A history of calculus Read the history of calculus withproblems and diagrams from the great thinkers. AP Calculus http://712educators.about.com/od/mathcalculus/

zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') About Education Secondary School Educators Curriculum and Lesson Plans ... Mathematics Calculus Home Essentials Daily Warm Ups Biography Menu ... Curricular How-To's for 7-12 Educators zau(256,152,145,'gob','http://z.about.com/5/ad/go.htm?gs='+gs,''); Curriculum and Lesson Plans Assessments Technology and Education Learning Theories ... Help zau(256,138,125,'el','http://z.about.com/0/ip/417/0.htm','');w(xb+xb); Stay Current Subscribe to the About Secondary School Educators newsletter. Search Secondary School Educators Calculus Ideas and information for Calculus teachers. Alphabetical Recent Up a category Sir Isaac Newton Biography Read the brief biography of one of the inventors of calculus. This biograpy was created using the biographical framework from your About Guide. Gottfried Wilhelm von Leibniz Biography Read more about the other inventor of calculus. He worked on the ideas of calculus but never reached the same fame of Sir Isaac Newton. A History of Calculus Read the history of calculus with problems and diagrams from the great thinkers. AP Calculus AP Calculus brought to you by the College Board. Find out all the up-to-date information on the Advanced Placement Calculus exam.

33. Calculus Sites A fairly large index of History of Mathematics topics from the University ofSt. Andrew, Scotland. One section is devoted to the history of calculus. http://www.rit.edu/~673www/calculusresources.html

Calculus Resources on the Web Sites and Directories of Sites for Calculus This page contains links to a variety of sites. Some sites have extensive directories while some links are to sites with particular modules devoted to calculus topics. We have tried to pull out those sites which we have found to have good quality and are relevant to difficult topics. Some are of particular importance for faculty, while others are aimed at students and still others would be valuable assets for both teachers and students. We leave you to decide which is which. The directories contain many useful links but, unfortunately, many not so useful and amateurish links. Again, you may decide which is which. Remember, as with all Web searches: You have to kiss a lot of frogs before you find your prince(ss). http://www.seresc.k12.nh.us/alvirne/apresc.html A directory of many, many sites which are calculus resources. Includes materials on graphing calculators and various software packages. http://mss.math.vanderbilt.edu/~pscrooke/toolkit.shtml Has links to good interactive modules on 15 calculus topics, including parametric equations and polar equations. Driven by Mathematica, it allows students to put in their own functions for analysis. It does not use Mathematica on the students computer, it accesses it at the site. It would be good for student use and for classroom examples, demonstration etc. http://clem.mscd.edu/~talmanl/MathAnim.html

34. Calculus@Internet A description of quadratic cubic and quartic equations in history The rise ofcalculus A description of the history of calculus and how it came about. http://www.calculus.net/ci2/search/?request=category&code=67&off=0&tag=920043892

35. AP Calculus Internet Resources Calculus, history. A history of calculus Part of a math history project at St.Andrews College; History of mathematics An outstanding history website. Algebra. http://www.hsd.k12.or.us/schools/ghs/staff/abel/homework/hwresource.html

Calculus home About the class Calculus parents Topics covered ... Study guide Internet resources Resource index General Math Calculus online tutorials and courses sites with exams ... Fun math links General math SOS Math Good list of problems with solutions Ask Dr. Math Dr. Math to the rescue The MathPage Dan's Math@Home Page Really great basic math skills here Basic College Mathematics Math Stories.com Very nice site with word problems for students grades 1-5 WebMath Math.com Homework Help AAA Math If you want to have fun learning math, then try this site Math for Morons Like Us Cool Math.com Definitely cool! Math Homework Helper Great math help for elementary and middle school students from Fact Monster Frank Potter's Science Gems - Mathematics Don't miss Mr. Potter's sites QuickMath Great for solving equations for algebra and calculus The Math Forum Wonderful math page with many math links and information You will find just about any kind of math here Harcourt Animated Math Glossary A definitely cool glossary of math terms Calculus, online tutorials and courses

36. Calculus: From Archimedes To Newton Calculus. From Archimedes to Newton. A Website About Biographies of ImportantFigures in the history of calculus. Brief Summary of the history of calculus. http://www.comp.nus.edu.sg/~liuzhich/Calculus/

Calculus From Archimedes to Newton A Website About Biographies of Important Figures in the History of Calculus About References Links Brief Summary of the History of Calculus Starting from ancient Greek, people have been searching for methods of finding areas and volumes of irregular shapes and bodies. Archimedes , intelligently considering bodies as made up of infinite thin slices, found the formulas for calculating the volumes of bodies like cone and sphere by using his famous balancing method. Later Cavalieri also divided the area into infinite lines. Their methods are often useful in obtaining results, but they are not always logically vigorous. The idea that infinte pieces whose thickness is can eventually made up a solid body is questionable. Another genre of questions related to calculus is finding the tangents, the maxima and the minima of the curves. Apollonius, Descartes , Fermat and Barrow devised their own methods of solving such problems. And Fermat and Barrow's methods also involved the use of infinitesimals which made their calculation logically deficient. The logical deficiency of the using of infinitesimals hindered the development of calculus until Newton came up with the idea of moving points making up a curve, thus getting rid of the use of infinitesimals.

37. LESSON PLANET - 30,000 Lessons And 86 Lesson Plans For Calculus 3. Calculus 12 Overview and history of calculus (Overview of Calculus) - It isexpected that students will understand that calculus was developed to help http://www.lessonplanet.com/search/Math/Calculus

Powered by Over 30,000 Lesson Plans, Teacher Tools and More! All Grades Pre-K K-2 Higher Ed Search the largest directory of lesson plans on the web! Attention Teachers! Join Lesson Planet Today! For only $9.95 (a year) gain full access to Lesson Planet's directory of 30,000+ lesson plans as a Lesson Planet Silver Member! For only $24.95 (a year), become a Gold Member and gain full access to 30,000+ lessons AND our TeacherWebTools suite of online tools (featuring TeacherSiteMaker, Online Storage, NewsletterMaker, LessonMaker and more!) Learn More TeacherWebTools: TeacherSiteMaker NewsletterMaker AssignmentMaker LessonMaker ... Your Account Teacher Web Resources: Current Top Sites Top Site Archives Curriculum Corners Maps Planet ... Calculus Found Calculus ' Lesson Plans. Also for ' Calculus 99 Web Sites 3 Videos * Log in or become a Lesson Planet Member to gain access to lesson plans. Lesson Plans (1 - 10 of 86): I Love Calculus - Okay, I admit it. I LOVE Calculus! IT'S HOT!!! AND it's Fun, AND it's a Challenge. Here are some Calculus LINKS- So Hot they'll Make Your T-1 Line Sizzle Grades: Calculus@Internet - Although this site is called Calculus@Internet and our main focus is on calculus, we are accumulating links for other mathematical subjects. Our goal is to develop a site which speaks to all mathematical subject areas. We are beginning with calculus and g

38. Calculus 17, Fall '96 History Figures History Figures for Math 17, Fall 96. This page contains some figuresfrom the history of calculus. Characters from the history of calculus. http://www.assumption.edu/Alfano/Calc17-F96/historyfigures.html

History Figures for Math 17, Fall '96 This page contains some figures from the history of Calculus. They would make very good subjects for the Web project due at the end of the semester. You are encouraged to investigate some of these characters, by searching the Web and/or local libraries. I encourage you to select a character that you haven't heard of before. If you select an easy target like Isaac Newton, you'll have to do a lot of writing to cover him completely. The lesser-known figures mentioned below also have interesting histories, and will make an easier report. All the History Figures Student Web Biography Projects Go to Calculus 17 home page Characters from the History of Calculus A small sample of characters are the following, mentioned in the excellent article The Rise of Calculus , from the MacTutor History of Mathematics archive . They are ordered by date of birth. Zeno of Elea (c.490 BC - c.430 BC) Leucippus (c.480 BC - c.420 BC) Antiphon the Sophist (480 BC - 411 BC) Democritus of Abdera (c.460 BC - c.370 BC) Eudoxus of Cnidus (408 BC - 355 BC) Archimedes of Syracuse (287 BC - 212 BC) Luca Valerio (1552 - 1618) Johannes Kepler (1571 - 1630) Rene Descartes (1596 - 1650) Bonaventura Francesco Cavalieri (1598-1647) Florimond de Beaune (1601 - 1652) Pierre de Fermat (1601 - 1665) Gilles Personne de Roberval (1602 - 1675) Evangelista Torricelli (1608 - 1647) Stefano degli Angeli (1623 - 1697) Pietro Mengoli (1626 - 1686) Robert Boyle (1627-1691) Johann van Waveren Hudde (1628 - 1704)

39. The History Of Calculus http://www.math.dartmouth.edu/~m1f01/timeline.html

40. Calculus History Interested in how Calculus became what it is today? This site offers a historical account of the progression of the study from its infancy to its present state. http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/The_rise_of_calculus.html

A history of the calculus Analysis index History Topics Index 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.

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