DOCSLIB.ORG

Algebra for the Sciences Textbook

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Algebra for the Sciences K.Oty B.Elliott August 6, 2018 i Preface This book was developed as an alternative to the traditional college algebra book currently used at many universities. The first edition was written while we were partially funded by a grant from the National Science Foundation and some of the projects in the second edition were written with the support of the Ok- lahoma IDeA Network of Biomedical Research Excellence (OK-INBRE) during the Summer of 2010. The motivation for this book was to find material for stu- dents who might not be continuing their studies in mathematics but who would need to apply mathematical skills to science courses. Additionally, we designed this book for elementary education majors to satisfy the algebra requirements as recommended by the National Council of Teachers in Mathematics (NCTM). We began the development of this book by having discussions with a variety of science faculty and asking what their expectations were for mathematical skills for students completing a college algebra course. It was enlightening to learn that many of the skills that our science colleagues expected of these stu- dents were not skills that were taught in a traditional college algebra course. The topics of estimation, unit conversions, geometry and extrapolation were the skills most often mentioned that were not covered in College Algebra. We have included these topics which makes our book quite different than a traditional algebra text. The other striking difference between our book and a traditional college al- gebra book is the use of demonstrations and projects. We wanted to motivate the students to study the mathematics by presenting a problem from a field of science that would use the particular mathematics. We have written these demonstrations so that no previous knowledge of the scientific principles in- volved are required from either the instructor or the student. By introducing the framework first we hope that this will motivate the students to study the mathematics and to address the perennial question “why do I need to learn this?” We include skill based exercises throughout the chapters so that students can check their progress. Instead of the traditional problem sets at the end of the chapter, we have compiled a list of projects that use the skills developed in the chapter. When possible, we have used real data sets and occasionally ask the student to collect the data themselves. The solutions to the projects are intended to be written reports using the mathematics and explaining the procedures and concepts. Typically we assign one or two projects per student. For some of the more involved projects that require data collection we might assign the project to a group. This book is used to teach a one semester course. We cover all of the material in that time. We do use class time for demonstrations, collaborative exercises, and for working with technology. The authors wish to acknowledge and recognize the significant work on the first edition by co-authors Dr. Bryan Clark and Dr. John McArthur. We also ii wish to thank Dr. Diane Dixon for contributing projects for the second edition. iii Technology Students will need to have access to either computer software or a graphing calculator that does linear, quadratic, and logarithmic or exponential regression. We have used both the statistical software JMP c , the TI-83 Plus graphing c calculator, and Mathematica in teaching this course. In teaching this course with a graphing calculator, it should be noted that starting in Chapter 4 we ask for the adjusted R2 value which the TI-83 Plus does not find. The questions can be modified appropriately but it is important to point out that comparing the R2 value between a linear and a quadratic fit, for example, is not an appropriate way to decide which one of the two curves fits the data better. We have included web addresses for projects that ask students to find addi- tional information before completing the project. However, with the fluidity of the world wide web, these addresses may change and the students might need to find the information at some other site. Supplements There is an instructor’s guide available to instructors who are using this book in teaching their course. It contains all the solutions to the problems and projects when possible. For the projects that rely on students collecting data or other information, we have included a grading guide in the instructor’s manual. Additionally, there is a list of equipment that is needed for the demonstrations and the projects. Appendices We have included three appendices with the book. The first, Appendix A, discusses basic scientific notation. Appendix B is a list of references and web sites for further information. The last appendix contains the answers to the odd problems. iv Contents 1 Estimation 1 1.1 Objectives: ............................... 1 1.2 Introduction: ............................. 1 1.3 Demonstration: ............................ 2 1.4 The Mathematics: .......................... 3 1.4.1 NumericalEstimation . 3 1.4.2 SamplingTechniques. 5 1.4.3 UnitConversions.. ... .... ... .... ... .... 7 1.5 Homework Projects: ......................... 12 2 Geometry 15 2.1 Objectives: ............................... 15 2.2 Motivation: .............................. 15 2.3 Introduction to Home Range and Territory: ............ 16 2.4 Demonstration: ............................ 18 2.5 The Mathematics: .......................... 19 2.5.1 Area.............................. 19 2.5.2 Perimeter ........................... 24 2.5.3 Volume ............................ 26 2.5.4 SurfaceArea ......................... 29 2.6 Homework Projects: ......................... 31 3 Lines 39 3.1 Objectives: ............................... 39 3.2 Motivation: .............................. 39 3.3 Introduction to Population Size Estimation: ............ 40 3.4 Demonstration: ............................ 42 3.5 The Mathematics: .......................... 43 3.5.1 Slope ............................. 43 3.5.2 TheEquationofaLine . 45 3.5.3 FindingSlopesandIntercepts . 47 3.5.4 Graphs ............................ 48 3.5.5 Functions ........................... 50 3.5.6 LinearRegression. 52 v vi CONTENTS 3.6 Extrapolation and Interpolation: ................... 56 3.7 Homework Projects: ......................... 58 4 Quadratics 67 4.1 Objectives: ............................... 67 4.2 Motivation: .............................. 67 4.3 Introduction to Kinematics: ..................... 68 4.4 Demonstration: ............................ 69 4.5 The Mathematics: .......................... 70 4.5.1 Vertex............................. 70 4.5.2 Intercepts ........................... 72 4.5.3 Graphs ............................ 74 4.5.4 Regression........................... 77 4.6 Homework Projects: ......................... 83 5 Exponentials 97 5.1 Objectives: ............................... 97 5.2 Motivation: .............................. 97 5.3 Introduction to Population Growth: ................. 98 5.4 Demonstration: ............................ 98 5.5 The Mathematics: ..........................100 5.5.1 IntegerExponents . 100 5.5.2 Graphs ............................105 5.6 Homework Projects: .........................107 6 Logarithms 115 6.1 Objectives: ...............................115 6.2 Motivation: ..............................115 6.3 Introduction to Sound: ........................116 6.4 Demonstration: ............................118 6.5 The Mathematics: ..........................119 6.5.1 Logarithms .......................... 119 6.5.2 CommonLogsandNaturalLogs . 122 6.5.3 Graphs ............................123 6.5.4 Equations........................... 125 6.5.5 RatesofGrowth . .... ... .... ... .... ... 127 6.6 Homework Projects: .........................130 7 Systems of Equations 139 7.1 Objectives: ...............................139 7.2 Motivation: ..............................139 7.3 Demonstration: ............................140 7.4 The Mathematics: ..........................141 7.4.1 TwoLinearEquations . 141 7.4.2 ThreeLinearEquations . 146 7.4.3 NonlinearSystems . 149 CONTENTS vii 7.5 Homework Projects: .........................153 A Scientific Notation 171 BReferencesandFurtherReadings 173 B.1 Chapter1 ............................... 173 B.1.1 BodyMassIndex. 173 B.1.2 EmpireStateBuilding . 173 B.1.3 Molarity............................ 173 B.2 Chapter2 ............................... 173 B.2.1 Bats .............................. 173 B.2.2 CMRMethod......................... 174 B.3 Chapter3 ............................... 174 B.3.1 Bodyweightversusranges. 174 B.3.2 TargetHeartRates. 174 B.4 Chapter4 ............................... 174 B.4.1 History ............................ 174 B.4.2 Reflectivityofwatersurfaces . 174 B.4.3 SpeciesDiversity . 175 B.4.4 PopulationDynamics . 175 B.5 Chapter5 ............................... 175 B.5.1 History ............................ 175 B.5.2 Population .......................... 175 B.5.3 WhoopingCranes . 175 B.6 Chapter6 ............................... 176 B.6.1 History ............................ 176 B.6.2 Titanium-44 .... ... .... ... .... ... .... 176 B.6.3 ShannonDiversityIndex. 176 B.7 Chapter7 ............................... 176 B.7.1 History ............................ 176 B.7.2 Population Growth versus Food Production . 176 B.7.3 Censusdata. .... ... .... ... .... ... .... 176 B.7.4 OxygenConsumption . 177 B.7.5 Bluebirds ........................... 177 C Answers to Odd Problems 179 C.1 Chapter1 ..............................
Recommended publications
  • Great Physicists

    Great Physicists

    Great Physicists Great Physicists The Life and Times of Leading Physicists from Galileo to Hawking William H. Cropper 1 2001 1 Oxford New York Athens Auckland Bangkok Bogota´ Buenos Aires Cape Town Chennai Dar es Salaam Delhi Florence HongKong Istanbul Karachi Kolkata Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi Paris Sao Paulo Shanghai Singapore Taipei Tokyo Toronto Warsaw and associated companies in Berlin Ibadan Copyright ᭧ 2001 by Oxford University Press, Inc. Published by Oxford University Press, Inc. 198 Madison Avenue, New York, New York 10016 Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Cropper, William H. Great Physicists: the life and times of leadingphysicists from Galileo to Hawking/ William H. Cropper. p. cm Includes bibliographical references and index. ISBN 0–19–513748–5 1. Physicists—Biography. I. Title. QC15 .C76 2001 530'.092'2—dc21 [B] 2001021611 987654321 Printed in the United States of America on acid-free paper Contents Preface ix Acknowledgments xi I. Mechanics Historical Synopsis 3 1. How the Heavens Go 5 Galileo Galilei 2. A Man Obsessed 18 Isaac Newton II. Thermodynamics Historical Synopsis 41 3. A Tale of Two Revolutions 43 Sadi Carnot 4. On the Dark Side 51 Robert Mayer 5. A Holy Undertaking59 James Joule 6. Unities and a Unifier 71 Hermann Helmholtz 7. The Scientist as Virtuoso 78 William Thomson 8.
  • Curren T Anthropology

    Curren T Anthropology

    Forthcoming Current Anthropology Wenner-Gren Symposium Curren Supplementary Issues (in order of appearance) t Humanness and Potentiality: Revisiting the Anthropological Object in the Anthropolog Current Context of New Medical Technologies. Klaus Hoeyer and Karen-Sue Taussig, eds. Alternative Pathways to Complexity: Evolutionary Trajectories in the Anthropology Middle Paleolithic and Middle Stone Age. Steven L. Kuhn and Erella Hovers, eds. y THE WENNER-GREN SYMPOSIUM SERIES Previously Published Supplementary Issues December 2012 HUMAN BIOLOGY AND THE ORIGINS OF HOMO Working Memory: Beyond Language and Symbolism. omas Wynn and Frederick L. Coolidge, eds. GUEST EDITORS: SUSAN ANTÓN AND LESLIE C. AIELLO Engaged Anthropology: Diversity and Dilemmas. Setha M. Low and Sally Early Homo: Who, When, and Where Engle Merry, eds. Environmental and Behavioral Evidence V Dental Evidence for the Reconstruction of Diet in African Early Homo olum Corporate Lives: New Perspectives on the Social Life of the Corporate Form. Body Size, Body Shape, and the Circumscription of the Genus Homo Damani Partridge, Marina Welker, and Rebecca Hardin, eds. Ecological Energetics in Early Homo e 5 Effects of Mortality, Subsistence, and Ecology on Human Adult Height 3 e Origins of Agriculture: New Data, New Ideas. T. Douglas Price and Plasticity in Human Life History Strategy Ofer Bar-Yosef, eds. Conditions for Evolution of Small Adult Body Size in Southern Africa Supplement Growth, Development, and Life History throughout the Evolution of Homo e Biological Anthropology of Living Human Populations: World Body Size, Size Variation, and Sexual Size Dimorphism in Early Homo Histories, National Styles, and International Networks. Susan Lindee and Ricardo Ventura Santos, eds.
  • Los Computadores, Esos Locos Cacharros

    Los Computadores, Esos Locos Cacharros

    LOS COMPUTADORES, ESOS LOCOS CACHARROS ACADEMIA DE INGENIERÍA LOS COMPUTADORES, ESOS LOCOS CACHARROS DISCURSO DEL ACADÉMICO EXCMO. SR. D. MATEO VALERO CORTÉS LEÍDO EN LA SESIÓN INAUGURAL DEL AÑO ACADÉMICO EL DÍA 30 DE ENERO DE 2003 MADRID MMIII Editado por la Academia de Ingeniería © 2003, Academia de Ingeniería © 2003 del texto, Mateo Valero Cortés ISBN: 84-95662-11-6 Depósito legal: M. 2.474-2003 Impreso en España LECCIÓN INAUGURAL DEL AÑO ACADÉMICO 2003 Excmos. Sres. Señoras y señores Queridos amigos, Deseo expresar mi gratitud al Presidente de la Academia, por sugerir mi nombre para dar esta lección inaugural de la Academia del año 2003, y a mis compañeros académicos por haber aceptado dicha invitación. Real - mente es un gran honor para mí el poder dirigirme a todos vosotros en el principio de este nuevo año. He decidido comentar algunos aspectos de los computadores. Estos “locos cacharros” han sido las máquinas que más han evolucionado en tan poco tiempo. Con apenas unos pocos más de cincuenta años de existencia, sus características han cambiado a una velocidad increíble. El responsable direc - to de este cambio ha sido el transistor. Este dispositivo, inventado hace cin - cuenta y cinco años, ha sido el verdadero protagonista de la sociedad de la información. Sin su descubrimiento, la informática y las comunicaciones no habrían avanzado apenas. A partir de él, se hace posible la revolución de las tecnologías de la Información y de las Comunicaciones que son las que más influencia han tenido en el avance de la humanidad. Muchos son los componentes de estas tecnologías.
  • TERRATEC Epbms Gear up for New Istanbul Metro Line

    TERRATEC Epbms Gear up for New Istanbul Metro Line

    PRESS RELEASE 1 MARCH 2020 For Immediate Release Release Number: 13169 TERRATEC EPBMs gear up for new Istanbul Metro line Gulermak, Nurol & Makyol JV is currently completing TBM testing on-site for the new Ümraniye-Ataşehir-Göztepe line, the latest addition to Istanbul’s metro expansion. TERRATEC is pleased to announce that it now has a total of nine machines working concurrently on Istanbul’s Metro system, in Turkey. The on-site assembly of two 6.56m diameter Earth Pressure Balance Tunnel Boring Machines (EPBMs) is currently underway for the Ümraniye-Ataşehir-Göztepe (UAG) Metro line, which is being constructed by the by the Gulermak, Nurol & Makyol JV. These EPBMs, along with another pair of sister machines that have already been assembled for this project, are all due to be launched and mining by mid-May. The 13km-long Ümraniye-Ataşehir-Göztepe (UAG) line, along with its 11 new stations and NATM-built connections, will form a second north to south rail corridor under the densely-populated Anatolian side of Istanbul and will be located entirely underground at an average depth of about 30m. The robust TERRATEC TBMs have versatile mixed-face dome-style cutterheads with an opening ratio of about 35% that have proven to work extremely effectively in Istanbul’s 171 Davey Street, Hobart, Tasmania 7000, AUSTRALIA | Tel +61 362233282 11F Wharf T&T Centre, 7 Canton Road, Kowloon, HONG KONG | Tel +852 31693660 Page | 1 PRESS RELEASE 1 MARCH 2020 mixed geology – which includes low-strength sandstones, siltstones, limestones and shales – as well as other state-of-the-art features such as VFD electric cutterhead drives, tungsten carbide soft ground cutting tools that are interchangeable with 17’’ roller disc cutters, high torque screw conveyors and active articulation systems.
  • EXP8449 Preliminary User's Manual

    EXP8449 Preliminary User's Manual

    EXP8449 Preliminary User’s Manual TABLE OF CONTENTS CHAPTER 1 INTRODUCTION..........................................1 1.1 OVERVIEW ...........................................................1 1.2 SYSTEM FEATURES ...........................................1 1.3 SYSTEM SPECIFICATION ...................................2 1.4 SYSTEM PERFORMANCE...................................2 1.5 EXP8449 BOARD LAYOUT ..................................3 CHAPTER 2 INSTALLATION ................................................4 2.1 DRAM INSTALLATION .........................................4 2.2 SRAM INSTALLATION .........................................6 2.3 CPU INSTALLATION ............................................8 2.3.1 CPU TYPE SELECTION .............................8 2.3.2 FREQUENCY SELECTION.......................19 2.4 OTHER JUMPER AND CONNECTOR INSTALLATION...........................................................22 CHAPTER 3 SYSTEM BIOS SETUP....................................25 3.1 SYSTEM SETUP.................................................27 3.2 UTILITY...............................................................39 3.3 DEFAULT ............................................................44 RMA FORM EXP8449 User’s Manual CHAPTER 1 INTRODUCTION 1.1 OVERVIEW The EXP8449 is complemented by a 512KB second level Write- Back cache providing workstation level computing performance, and SIMM sockets support up to 64MB of DRAM. The EXP8449 motherboard offers outstanding I/O capabilities. Three PCI Local Bus slots provide a high bandwidth data path
  • A Brief History of Microwave Engineering

    A Brief History of Microwave Engineering

    A BRIEF HISTORY OF MICROWAVE ENGINEERING S.N. SINHA PROFESSOR DEPT. OF ELECTRONICS & COMPUTER ENGINEERING IIT ROORKEE Multiple Name Symbol Multiple Name Symbol 100 hertz Hz 101 decahertz daHz 10–1 decihertz dHz 102 hectohertz hHz 10–2 centihertz cHz 103 kilohertz kHz 10–3 millihertz mHz 106 megahertz MHz 10–6 microhertz µHz 109 gigahertz GHz 10–9 nanohertz nHz 1012 terahertz THz 10–12 picohertz pHz 1015 petahertz PHz 10–15 femtohertz fHz 1018 exahertz EHz 10–18 attohertz aHz 1021 zettahertz ZHz 10–21 zeptohertz zHz 1024 yottahertz YHz 10–24 yoctohertz yHz • John Napier, born in 1550 • Developed the theory of John Napier logarithms, in order to eliminate the frustration of hand calculations of division, multiplication, squares, etc. • We use logarithms every day in microwaves when we refer to the decibel • The Neper, a unitless quantity for dealing with ratios, is named after John Napier Laurent Cassegrain • Not much is known about Laurent Cassegrain, a Catholic Priest in Chartre, France, who in 1672 reportedly submitted a manuscript on a new type of reflecting telescope that bears his name. • The Cassegrain antenna is an an adaptation of the telescope • Hans Christian Oersted, one of the leading scientists of the Hans Christian Oersted nineteenth century, played a crucial role in understanding electromagnetism • He showed that electricity and magnetism were related phenomena, a finding that laid the foundation for the theory of electromagnetism and for the research that later created such technologies as radio, television and fiber optics • The unit of magnetic field strength was named the Oersted in his honor.
  • The HP Apollo 9000 Model 706 Is a New Low-End, PA-RISC Station for the Entry-Level Market. the HP Standard Instrument Control Li

    The HP Apollo 9000 Model 706 Is a New Low-End, PA-RISC Station for the Entry-Level Market. the HP Standard Instrument Control Li

    The HP Apollo 9000 Model 706 is a new low-end, PA-RISC based color work- station for the entry-level market. See ~e S8 The HP Standard Instrument Control Library is an W) library for inetnunent control av~lications on HP ~I;oio ISeries 700 and HP 9000 Model V. controllers. See page 2% New network-ready HP Vectra 38WSW PC - latest addition to HP's network-ready PC family. See page $4 HP OpenView Release 3 - the next generation of network and system nuuraRement *pa0 New HP DTC represents a signitlat step toward making the DTCthechosen server for HP-UX. HEWLETT PACKARD i -'. -. , - 8 KP Computer Update, June 1992 HP Computer Museum www.hpmuseum.net For research and education purposes only. In This Issue Management Perspective HP 3000 field upgrade HP Apollo 9000 Series 700 5 changes Dud CRX multimonitor HP Premier Account Support upgrade General News NetBase brings disaster HP NCS 2 for Domain and 7 Events tolerance to HP 3000 OSF/l Strategic concerns of New HP TurboSTORWfi 11 SoftPC 3.0 now shipping on HP users trial copy Series 700 and 800 HP executive management Peer-tepeer connectivity for HP FTM9000 on HP Apollo seminar HP LU 6.2 APVXL 9000 Series 700 U.K. object orientation and Return credits for high-end Wingz, Island Graphics, and ObjectIQ seminar series memory and 110 add-on Lotus obsolescence products Promotions Reduced high-end memory HP 1000 Systems 9 prices 33 HP 1000 A-Series microfloppy discontinuance HP 3000 Systems HP 9000 Systems 12 The open HP 3000 - the best 23 Making sense of the standards Personal Computers commercial
  • 2019 Annual Report Annual 2019

    2019 Annual Report Annual 2019

    a force for good. 2019 ANNUAL REPORT ANNUAL 2019 1, cours Ferdinand de Lesseps 92851 Rueil Malmaison Cedex – France Tel.: +33 1 47 16 35 00 Fax: +33 1 47 51 91 02 www.vinci.com VINCI.Group 2019 ANNUAL REPORT VINCI @VINCI CONTENTS 1 P r o l e 2 Album 10 Interview with the Chairman and CEO 12 Corporate governance 14 Direction and strategy 18 Stock market and shareholder base 22 Sustainable development 32 CONCESSIONS 34 VINCI Autoroutes 48 VINCI Airports 62 Other concessions 64 – VINCI Highways 68 – VINCI Railways 70 – VINCI Stadium 72 CONTRACTING 74 VINCI Energies 88 Eurovia 102 VINCI Construction 118 VINCI Immobilier 121 GENERAL & FINANCIAL ELEMENTS 122 Report of the Board of Directors 270 Report of the Lead Director and the Vice-Chairman of the Board of Directors 272 Consolidated nancial statements This universal registration document was filed on 2 March 2020 with the Autorité des Marchés Financiers (AMF, the French securities regulator), as competent authority 349 Parent company nancial statements under Regulation (EU) 2017/1129, without prior approval pursuant to Article 9 of the 367 Special report of the Statutory Auditors on said regulation. The universal registration document may be used for the purposes of an offer to the regulated agreements public of securities or the admission of securities to trading on a regulated market if accompanied by a prospectus or securities note as well as a summary of all 368 Persons responsible for the universal registration document amendments, if any, made to the universal registration document. The set of documents thus formed is approved by the AMF in accordance with Regulation (EU) 2017/1129.
  • John Napier's Life Napier's Logarithms KYLIE BRYANT & PAUL SCOTT

    John Napier's Life Napier's Logarithms KYLIE BRYANT & PAUL SCOTT

    KYLIE BRYANT & PAUL SCOTT John Napier’s life Napier’s logarithms John Napier was born in 1550 in the Tower of Napier’s idea in inventing the logarithm was to Merchiston, near Edinburgh, Scotland. His save mathematicians from having to do large father, Archibald Napier, was knighted in 1565 calculations. These days, calculations and was appointed Master of the Mint in 1582. involving large numbers are done using calcu- His mother, Janet Bothwell, was the sister of lators or computers; however before these were the Bishop of Orkney. Napier’s was an impor- invented, large calculations meant that much tant family in Scotland, and had owned the time was taken and mistakes were made. Merchiston estate since 1430. Napier’s logarithm was not defined in terms Napier was educated at St Salvator’s of exponents as our logarithm is today. College, graduating in 1563. He was just 13 Instead Napier thought of his logarithm in years old when his mother died and he was terms of moving particles, distances and veloc- sent to St Andrew’s University where he ities. He considered two lines, AZ of fixed studied for two years. This is where he gained length and A'Z' of infinite length and points X his interest in theology. He did not graduate, and X' starting at A and A' moving to the right however, instead leaving to travel around with the same initial velocity. X' has constant Europe for the next five years. During this velocity and X has a velocity proportional to time he gained knowledge of mathematics and the distance from X to Z.
  • The Logarithmic Tables of Edward Sang and His Daughters

    The Logarithmic Tables of Edward Sang and His Daughters

    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Historia Mathematica 30 (2003) 47–84 www.elsevier.com/locate/hm The logarithmic tables of Edward Sang and his daughters Alex D.D. Craik School of Mathematics & Statistics, University of St Andrews, St Andrews, Fife KY16 9SS, Scotland, United Kingdom Abstract Edward Sang (1805–1890), aided only by his daughters Flora and Jane, compiled vast logarithmic and other mathematical tables. These exceed in accuracy and extent the tables of the French Bureau du Cadastre, produced by Gaspard de Prony and a multitude of assistants during 1794–1801. Like Prony’s, only a small part of Sang’s tables was published: his 7-place logarithmic tables of 1871. The contents and fate of Sang’s manuscript volumes, the abortive attempts to publish them, and some of Sang’s methods are described. A brief biography of Sang outlines his many other contributions to science and technology in both Scotland and Turkey. Remarkably, the tables were mostly compiled in his spare time. 2003 Elsevier Science (USA). All rights reserved. Résumé Edward Sang (1805–1890), aidé seulement par sa famille, c’est à dire ses filles Flora et Jane, compila des tables vastes des logarithmes et des autres fonctions mathématiques. Ces tables sont plus accurates, et plus extensives que celles du Bureau du Cadastre, compileés les années 1794–1801 par Gaspard de Prony et une foule de ses aides. On ne publia qu’une petite partie des tables de Sang (comme celles de Prony) : ses tables du 1871 des logarithmes à 7-places décimales.
  • November 2019

    November 2019

    A selection of some recent arrivals November 2019 Rare and important books & manuscripts in science and medicine, by Christian Westergaard. Flæsketorvet 68 – 1711 København V – Denmark Cell: (+45)27628014 www.sophiararebooks.com AMPÈRE, André-Marie. THE FOUNDATION OF ELECTRO- DYNAMICS, INSCRIBED BY AMPÈRE AMPÈRE, Andre-Marie. Mémoires sur l’action mutuelle de deux courans électri- ques, sur celle qui existe entre un courant électrique et un aimant ou le globe terres- tre, et celle de deux aimans l’un sur l’autre. [Paris: Feugeray, 1821]. $22,500 8vo (219 x 133mm), pp. [3], 4-112 with five folding engraved plates (a few faint scattered spots). Original pink wrappers, uncut (lacking backstrip, one cord partly broken with a few leaves just holding, slightly darkened, chip to corner of upper cov- er); modern cloth box. An untouched copy in its original state. First edition, probable first issue, extremely rare and inscribed by Ampère, of this continually evolving collection of important memoirs on electrodynamics by Ampère and others. “Ampère had originally intended the collection to contain all the articles published on his theory of electrodynamics since 1820, but as he pre- pared copy new articles on the subject continued to appear, so that the fascicles, which apparently began publication in 1821, were in a constant state of revision, with at least five versions of the collection appearing between 1821 and 1823 un- der different titles” (Norman). The collection begins with ‘Mémoires sur l’action mutuelle de deux courans électriques’, Ampère’s “first great memoir on electrody- namics” (DSB), representing his first response to the demonstration on 21 April 1820 by the Danish physicist Hans Christian Oersted (1777-1851) that electric currents create magnetic fields; this had been reported by François Arago (1786- 1853) to an astonished Académie des Sciences on 4 September.
  • The Mathematical Work of John Napier (1550-1617)

    The Mathematical Work of John Napier (1550-1617)

    BULL. AUSTRAL. MATH. SOC. 0IA40, 0 I A45 VOL. 26 (1982), 455-468. THE MATHEMATICAL WORK OF JOHN NAPIER (1550-1617) WILLIAM F. HAWKINS John Napier, Baron of Merchiston near Edinburgh, lived during one of the most troubled periods in the history of Scotland. He attended St Andrews University for a short time and matriculated at the age of 13, leaving no subsequent record. But a letter to his father, written by his uncle Adam Bothwell, reformed Bishop of Orkney, in December 1560, reports as follows: "I pray you Sir, to send your son John to the Schools either to France or Flanders; for he can learn no good at home, nor gain any profit in this most perilous world." He took an active part in the Reform Movement and in 1593 he produced a bitter polemic against the Papacy and Rome which was called The Whole Revelation of St John. This was an instant success and was translated into German, French and Dutch by continental reformers. Napier's reputation as a theologian was considerable throughout reformed Europe, and he would have regarded this as his chief claim to scholarship. Throughout the middle ages Latin was the medium of communication amongst scholars, and translations into vernaculars were the exception until the 17th and l8th centuries. Napier has suffered badly through this change, for up till 1889 only one of his four works had been translated from Latin into English. Received 16 August 1982. Thesis submitted to University of Auckland, March 1981. Degree approved April 1982. Supervisors: Mr Garry J. Tee Professor H.A.