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Newton and Leibniz: the Development of Calculus Isaac Newton (1642-1727)
Newton and Leibniz: The development of calculus Isaac Newton (1642-1727) Isaac Newton was born on Christmas day in 1642, the same year that Galileo died. This coincidence seemed to be symbolic and in many ways, Newton developed both mathematics and physics from where Galileo had left off. A few months before his birth, his father died and his mother had remarried and Isaac was raised by his grandmother. His uncle recognized Newton’s mathematical abilities and suggested he enroll in Trinity College in Cambridge. Newton at Trinity College At Trinity, Newton keenly studied Euclid, Descartes, Kepler, Galileo, Viete and Wallis. He wrote later to Robert Hooke, “If I have seen farther, it is because I have stood on the shoulders of giants.” Shortly after he received his Bachelor’s degree in 1665, Cambridge University was closed due to the bubonic plague and so he went to his grandmother’s house where he dived deep into his mathematics and physics without interruption. During this time, he made four major discoveries: (a) the binomial theorem; (b) calculus ; (c) the law of universal gravitation and (d) the nature of light. The binomial theorem, as we discussed, was of course known to the Chinese, the Indians, and was re-discovered by Blaise Pascal. But Newton’s innovation is to discuss it for fractional powers. The binomial theorem Newton’s notation in many places is a bit clumsy and he would write his version of the binomial theorem as: In modern notation, the left hand side is (P+PQ)m/n and the first term on the right hand side is Pm/n and the other terms are: The binomial theorem as a Taylor series What we see here is the Taylor series expansion of the function (1+Q)m/n. -
Metric System Units of Length
Math 0300 METRIC SYSTEM UNITS OF LENGTH Þ To convert units of length in the metric system of measurement The basic unit of length in the metric system is the meter. All units of length in the metric system are derived from the meter. The prefix “centi-“means one hundredth. 1 centimeter=1 one-hundredth of a meter kilo- = 1000 1 kilometer (km) = 1000 meters (m) hecto- = 100 1 hectometer (hm) = 100 m deca- = 10 1 decameter (dam) = 10 m 1 meter (m) = 1 m deci- = 0.1 1 decimeter (dm) = 0.1 m centi- = 0.01 1 centimeter (cm) = 0.01 m milli- = 0.001 1 millimeter (mm) = 0.001 m Conversion between units of length in the metric system involves moving the decimal point to the right or to the left. Listing the units in order from largest to smallest will indicate how many places to move the decimal point and in which direction. Example 1: To convert 4200 cm to meters, write the units in order from largest to smallest. km hm dam m dm cm mm Converting cm to m requires moving 4 2 . 0 0 2 positions to the left. Move the decimal point the same number of places and in the same direction (to the left). So 4200 cm = 42.00 m A metric measurement involving two units is customarily written in terms of one unit. Convert the smaller unit to the larger unit and then add. Example 2: To convert 8 km 32 m to kilometers First convert 32 m to kilometers. km hm dam m dm cm mm Converting m to km requires moving 0 . -
Donations to the Library 2000S
DONATIONS TO THE LIDRARY 277 DONATIONS TO THE LIBRARY Michael Andrews (BA 1960) The birth of Europe, 1991; The flight of the condor, 1982; The life that lives on Man, 1977 13 May 1999 - 12 May 2000 Anthony Avis (BA 1949) The Librarian is always delighted to hear from any member of the Gaywood past: some historical notes, 1999; The journey: reflective essays, College considering a gift of books, manuscripts, maps or photographs 1999 to the College Library. Brigadier David Baines Abdus Salam International Centre Documents relating to the army career of Alan Menzies Hiller A. M. Hamende (ed.), Tribute to Abdus Salam (Abdus Salam Memorial (matric. 1913), who was killed in action near Arras in May 1915 meeting, 19-22 Nov. 1997), 1999 D.M. P. Barrere (BA 1966) David Ainscough Georges Bernanos, 'Notes pour ses conferences' (MS), n. d. Chambers' guide to the legal profession 1999-2000, 1999 P. J. Toulet, La jeune fille verte, 1918 Robert Ganzo, Histoire avant Sumer, 1963; L'oeuvre poetique, 1956 Dr Alexander G. A.) Romain Rolland, De Jean Christophe a Colas Breugnon: pages de journal, Automobile Association, Ordnance Survey illustrated atlas of Victorian 1946; La Montespan: drame en trois actes, 1904 and Edwardian Britain, 1991 Ann MacSween and Mick Sharp, Prehistoric Scotland, 1989 Martyn Barrett (BA 1973) Antonio Pardo, The world of ancient Spain, 1976 Martyn Barrett (ed.), The development of language, 1999 Edith Mary Wightrnan, Galla Belgica, 1985 Gerard Nicolini, The ancient Spaniards, 1974 Octavian Basca Herman Ramm, The Parisi, 1978 Ion Purcaru and Octavian Basca, Oameni, idei, fapte din istoria J. -
1) What Is Another Name for the Enlightenment Period? 2
Name: Period: Enlightenment Video Review All about the Enlightenment: 1) What is another name for the Enlightenment period? 2) What was the time period of the Enlightenment? 3) What does the word Enlightenment mean and what is reason? The Scientific Method: 1) What do many scholars believe about Francis Bacon and Rene Descartes? 2) Where was Francis Bacon from, what did he believe about science and what was his approach to science based on? 3) Where was Rene Descartes from, and what did the book he published proclaim? 4) What new type of mathematics did Rene Descartes invent? 5) What did the discoveries of Bacon and Descartes lead to? The World of Isaac Newton: 1) What era did the Scientific Method helped to bring about? 2) Where was Isaac Newton from, and at which college did Francis Bacon and he study? 3) What branch of mathematics did Isaac Newton create? 4) What laws did Newton understand and mathematically formulate and how did he discover these laws? Even More Enlightenment Science: 1) What invention helped to extend the study of biology? 2) The English Biologist Robert Hooke discovered cells, what is a cell? 3) What did the English scientist William Harvey discover? 4) The Swedish botanist Carolus Linnaeus discovered the terms classifying and taxonomy what do these terms mean? Name: Period: Enlightenment Philosophers: 1) What were people like Isaac Newton and Carolus Linnaeus known as? 2) Where was John Locke from, and what did he believe about the power of a government? 3) What were the three natural rights that John Locke believed -
Gravity and Coulomb's
Gravity operates by the inverse square law (source Hyperphysics) A main objective in this lesson is that you understand the basic notion of “inverse square” relationships. There are a small number (perhaps less than 25) general paradigms of nature that if you make them part of your basic view of nature they will help you greatly in your understanding of how nature operates. Gravity is the weakest of the four fundamental forces, yet it is the dominant force in the universe for shaping the large-scale structure of galaxies, stars, etc. The gravitational force between two masses m1 and m2 is given by the relationship: This is often called the "universal law of gravitation" and G the universal gravitation constant. It is an example of an inverse square law force. The force is always attractive and acts along the line joining the centers of mass of the two masses. The forces on the two masses are equal in size but opposite in direction, obeying Newton's third law. You should notice that the universal gravitational constant is REALLY small so gravity is considered a very weak force. The gravity force has the same form as Coulomb's law for the forces between electric charges, i.e., it is an inverse square law force which depends upon the product of the two interacting sources. This led Einstein to start with the electromagnetic force and gravity as the first attempt to demonstrate the unification of the fundamental forces. It turns out that this was the wrong place to start, and that gravity will be the last of the forces to unify with the other three forces. -
Boris Jardine, 'Paper Tools', Forthcoming in Studies in History
Boris Jardine, ‘Paper Tools’, forthcoming in Studies in History and Philosophy of Science 64 (2017) Title: Paper Tools Author: Boris Jardine, University of Cambridge, Department of History and Philosophy of Science/Whipple Museum, Free School Lane, CB2 3RH Publication details: Studies in History and Philosophy of Science 64 (2017) Suppose I say to Turing, ‘This is the Greek letter sigma’, pointing to the sign σ. Then when I say, ‘Show me a Greek sigma in this book’, he cuts out the sign I showed him and puts it in this book.—Actually these things don’t happen. (Ludwig Wittgenstein, Lectures on the Foundations of Mathematics1) I begin with two vignettes from the early years of the Royal Society. First, on May 7th, 1673, a typically garrulous Robert Hooke delivered a short lecture to the Society entitled ‘Concerning Arithmetick Instruments’.2 This was an attack on a group of calculating instruments that had recently been invented and demonstrated by Samuel Morland, Leibniz and others. Earlier in the year, when Hooke had first seen Morland’s mechanical calculator, he had written in his diary the terse comment that it was ‘Very Silly’.3 In the lecture he gave full flight to his ire: As for ye Arithmeticall instrument which was produced here before this Society. It seemd to me so complicated with wheeles, pinions, cantrights [sic], springs, screws, stops & truckles, that I could not conceive it ever to be of any great use (quoted in Birch, 1756–7, p. 87) Why was the great philosopher of mechanism so unimpressed with this mathematical machine? The answer, elaborated in the Royal Society lecture, is as much about Hooke’s love of paper as his disdain for unnecessary and expensive instrumentation. -
The International Bureau of Weights and Measures 1875-1975
The International Bureau of Weights and Measures 1875-1975 U.S. DEPARTMENT OF COMMERCE National Bureau of Standards ""EAU of NBS SPECIAL PUBLICATION 420 Aerial view of the Pavilion de Breteuil and the immediate environs. To the east, the Seine and the Pont de Sevres; to the northwest, the Pare de Saint-Cloud: between the Pavilion de Breteuil (circled) and the bridge: the Manufacture Nationale de Porcelaine de Sevres. The new laboratories (1964) are situated north of the circle and are scarcely visible; they were built in a way to preserve the countryside. (Document Institute (leographique National, Paris). Medal commeiiKiraUn-i the centennial (if the Convention cif tlie Metre and the International Bureau of Weights and Measures. (Desifined by R. Corbin. Monnaie de Paris) The International Bureau of Weights and Measures 1875-1975 Edited by Chester H. Page National Bureau of Standards, U.S.A. and Pan I Vigoiireiix National Physieal Laboratory, U.K. Translation of tlie BIPM Centennial Volume Piibli>lieH on the ocrasioii <>( the lOOth Aniiiver^ai y ol tlie Treaty of tlie Metre May 20, 1975 U.S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Direcior Issued May 1 975 National Bureau of Standards Special Publication 420 Nat. Bur. Stand. (U.S.), Spec. Publ. 420. 256 pages (May 1975) CODEN: XNBSAV U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1975 For sale by the Superintendent of Documents U.S. Government Printing Office, Washington, D.C. 20402 Paper cover Price $3.00 Stock Number 003-003-01408 Catalog Number C13.10:420 FOREWORD The metric system was made legal by Congress in 1866, the United States of America signed the Treaty of the Metre in 1875, and we have been active in international coordination of measurements since that time. -
Metric System.Pdf
METRIC SYSTEM THE METRIC SYSTEM The metric system is much easier. All metric units are related by factors of 10. Nearly the entire world (95%), except the United States, now uses the metric system. Metric is used exclusively in science. Because the metric system uses units related by factors of ten and the types of units (distance, area, volume, mass) are simply-related, performing calculations with the metric system is much easier. METRIC CHART Prefix Symbol Factor Number Factor Word Kilo K 1,000 Thousand Hecto H 100 Hundred Deca Dk 10 Ten Base Unit Meter, gram, liter 1 One Deci D 0.1 Tenth Centi C 0.01 Hundredth Milli M 0.001 Thousandth The metric system has three units or bases. Meter – the basic unit used to measure length Gram – the basic unit used to measure weight Liter – the basic unit used to measure liquid capacity (think 2 Liter cokes!) The United States, Liberia and Burma (countries in black) have stuck with using the Imperial System of measurement. You can think of “the metric system” as a nickname for the International System of Units, or SI. HOW TO REMEMBER THE PREFIXES Kids Kilo Have Hecto Dropped Deca Over base unit (gram, liter, meter) Dead Deci Converting Centi Metrics Milli Large Units – Kilo (1000), Hecto (100), Deca (10) Small Units – Deci (0.1), Centi (0.01), Milli (0.001) Because you are dealing with multiples of ten, you do not have to calculate anything. All you have to do is move the decimal point, but you need to understand what you are doing when you move the decimal point. -
Rtusaeatz Nt,Rnasiivene
THE EVENING STAR. 38488 RQQe PUBLISRIED I AILY, Except Sunday, AT THE STAR BUILDINGS, any mznslo to sen e ear.te war to Avene, Corner 11th Street, 0011T the2ing f 1a0 tothi6 clany, it is Pensaylrania by partinenty as And why aboud as me '1he Evening Star Newspaper Oompany. King at sia1 reCeve the same alten as did 4:EQRUE W. ADAMS, Pres'r. one of his subjeCm alG the representative of a Tn EvrtNan Sra i. P.red to niscribers in the royal line, who, being aocredite to the paent r ty l. ,arr rP, on ti.eir own ateount, at 10 eents amInstmration, was, at the requet of Mr. 1 er w.ak or 44 eente per wonth. Colies at the Sicmes, our consul at Bangkok, sent from Siam eT:nt; r. - cnte each. by wail-sjotaKe prel aid- on one of our naval veeea, was received by toa eente a Llouth ; ene ye,r, $6; six months, I3. the iEterPd at the Poet Office t Washington, 0., President and Mrs. Hayes at the White -ase no. ca- mail ntatter 1 Housewith effusion, entertained there by them 'Ia V.1KT ST-r-p>b ished on F.atay-*2 a and mated asa member of thefamily for a con- errst trive irni;+i. Six months, 4; 10 copies siderable lenah of time? Every attention was for j1.: 20 col, . f.r $.. ARCH lavished on this myal guest; and should not the WAll nail ";bsCriltloine meit be paid in ad- CEN handsome young King receive as much? Yet It nee; > pa r ent l.ug than o paid for. -
Recruitment of LC3 to Damaged Golgi Apparatus
Cell Death & Differentiation (2019) 26:1467–1484 https://doi.org/10.1038/s41418-018-0221-5 ARTICLE Recruitment of LC3 to damaged Golgi apparatus 1,2,3 4 2,3 2,3 5,6 Lígia C. Gomes-da-Silva ● Ana Joaquina Jimenez ● Allan Sauvat ● Wei Xie ● Sylvie Souquere ● 4 7 8,9 8,9 1 2,3 Séverine Divoux ● Marko Storch ● Baldur Sveinbjørnsson ● Øystein Rekdal ● Luis G. Arnaut ● Oliver Kepp ● 2,3,10,11,12,13 4 Guido Kroemer ● Franck Perez Received: 11 May 2018 / Accepted: 8 October 2018 / Published online: 22 October 2018 © ADMC Associazione Differenziamento e Morte Cellulare 2018 Abstract LC3 is a protein that can associate with autophagosomes, autolysosomes, and phagosomes. Here, we show that LC3 can also redistribute toward the damaged Golgi apparatus where it clusters with SQSTM1/p62 and lysosomes. This organelle-specific relocation, which did not involve the generation of double-membraned autophagosomes, could be observed after Golgi damage was induced by various strategies, namely (i) laser-induced localized cellular damage, (ii) local expression of peroxidase and exposure to peroxide and diaminobenzidine, (iii) treatment with the Golgi-tropic photosensitizer redaporfin and light, (iv) or exposure to the Golgi-tropic anticancer peptidomimetic LTX-401. Mechanistic exploration led to the conclusion that both reactive oxygen species-dependent and -independent Golgi damage induces a similar phenotype that 1234567890();,: 1234567890();,: depended on ATG5 yet did not depend on phosphatidylinositol-3-kinase catalytic subunit type 3 and Beclin-1. Interestingly, knockout of ATG5 sensitized cells to Golgi damage-induced cell death, suggesting that the pathway culminating in the relocation of LC3 to the damaged Golgi may have a cytoprotective function. -
Gottfried Wilhelm Leibniz (1646-1716)
Gottfried Wilhelm Leibniz (1646-1716) • His father, a professor of Philosophy, died when he was small, and he was brought up by his mother. • He learnt Latin at school in Leipzig, but taught himself much more and also taught himself some Greek, possibly because he wanted to read his father’s books. • He studied law and logic at Leipzig University from the age of fourteen – which was not exceptionally young for that time. • His Ph D thesis “De Arte Combinatoria” was completed in 1666 at the University of Altdorf. He was offered a chair there but turned it down. • He then met, and worked for, Baron von Boineburg (at one stage prime minister in the government of Mainz), as a secretary, librarian and lawyer – and was also a personal friend. • Over the years he earned his living mainly as a lawyer and diplomat, working at different times for the states of Mainz, Hanover and Brandenburg. • But he is famous as a mathematician and philosopher. • By his own account, his interest in mathematics developed quite late. • An early interest was mechanics. – He was interested in the works of Huygens and Wren on collisions. – He published Hypothesis Physica Nova in 1671. The hypothesis was that motion depends on the action of a spirit ( a hypothesis shared by Kepler– but not Newton). – At this stage he was already communicating with scientists in London and in Paris. (Over his life he had around 600 scientific correspondents, all over the world.) – He met Huygens in Paris in 1672, while on a political mission, and started working with him. -
Report to AID on a Philippines Survey on Standardization and Measurement Services
TECH NATL INST OF STAND & NIST PUBLICATIONS A111D? OSfilb^ IMBSIR 76-1083 Report to AID on a Philippines Survey on Standardization and Measurement Services Edited by: H. Steffen Peiser Robert S. Marvin Office of International Relations National Bureau of Standards Washington, D. C. 20234 Conducted May 4 17, 1975 Issued June 1 976 The Survey was conducted as a part of the program under the US/NBS/Agency for International Development PASA TA(CE) 5-71 \ epared for gency for International Development * 7L'/b83 epartment of State jCj^ Washington, D. C. 20523 NBSIR 76-1083 REPORT TO AID ON A PHILIPPINES SURVEY ON STANDARDIZATION AND MEASUREMENT SERVICES Edited by: H. Steffen Peiser Robert S. Marvin Office of International Relations National Bureau of Standards Washington, D. C. 20234 Conducted May 4 - 17, 1975 Issued June 1 976 The Survey was conducted as a part of the program under the US/NBS/Agency for International Development PASA TA(CE) 5-71 Prepared for Agency for International Development Department of State Washington, D. C. 20523 U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary Dr. Betsy Ancfcer-Johrtsor At**st*nt Secretly for Science end Technology NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Acting Director i TABLE OF CONTENTS Paee PARTICIPANTS 1 I INTRODUCTION 4 II RECOMMENDATIONS - SUMMARIZED 6 III THE JOINT PROGRAM OF THE SURVEY TEAM 12 IV REPORT OF GROUP A, TECHNICAL STANDARDS COMMITTEE MANAGEMENT, Group Leader; Dr. Kenneth S. Stephens, School of Industrial & Systems Engineering and Industrial Development Division, Engr. Exp. Station, Georgia Institute of Technology, Atlanta, Georgia 29 V REPORT OF GROUP B, METRICATION Group Leader; Mr.