James Clerk Maxwell
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The History and Development of Numerical Analysis in Scotland: a Personal Perspective∗
The history and development of numerical analysis in Scotland: a personal perspective∗ G. A. Watson, Division of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland. Abstract An account is given of the history and development of numerical analysis in Scotland. This covers, in particular, activity in Edinburgh in the first half of the 20th century, the collaboration between Edinburgh and St Andrews in the 1960s, and the role played by Dundee from the 1970s. I will give some reminiscences from my own time at both Edinburgh and Dundee. 1 Introduction To provide a historical account of numerical analysis (or of anything else), it is necessary to decide where to begin. If numerical analysis is defined to be the study of algorithms for the problems of continuous mathematics [16], then of course it has a very long history (see, for example, [6], [13]). But \modern" numerical analysis is inextricably linked with computing machines. It is usually associated with programmable electronic computers, and is often said to have its origins in the 1947 paper by von Neumann and Goldstine [10]. The name apparently was first used around that time, and was given formal recognition in the setting up of the Institute for Numerical Analysis, located on the campus of the University of California at Los Angeles [3]. This was a section of the National Applied Mathematics Laboratories of the National Bureau of Standards, headed by J. H. Curtiss, who is often given credit for the name. Others consider modern numerical analysis to go back further than this; for example Todd [15] suggests it begins around 1936, and cites papers by Comrie and Turing. -
JAMES Maccullagh (1809-1847)
Hidden gems and Forgotten People ULSTER HISTORY CIRCLE JAMES MacCULLAGH (1809-1847) James MacCullagh, the eldest of twelve children, was born in the townland of Landahussy in the parish of Upper Badoney, Co. Tyrone in 1809. He was to become one of Ireland and Europe's most significant mathematicians and physicists. He entered Trinity College, Dublin aged just 15 years and became a fellow in 1832. He was accepted as a member of the Royal Irish Academy in 1833 before attaining the position of Professor of Mathematics in 1834. He was an inspiring teacher who influenced a generation of students, some of whom were to make their own contributions to the subjects. He held the position of Chair of Mathematics from 1835 to 1843 and later Professor of Natural and Experimental Philosophy from 1843 to 1847. In 1838 James MacCullagh was awarded the Royal Irish Academy's Cunningham Medal for his work 'On the laws of crystalline reflexion'. In 1842, a year prior to his becoming a fellow of the Royal Society, London, he was awarded their Copley Medal for his work 'On surfaces of the second order'. He devoted much of the remainder of his life to the work of the Royal Irish Academy. James MacCullagh's interests went beyond mathematical physics. He played a key role in building up the Academy's collection of Irish antiquities, now housed in the National Museum of Ireland. Although not a wealthy man, he purchased the early 12th century Cross of Cong, using what was at that time, his life savings. In August 1847 he stood unsuccessfully as a parliamentary candidate for one of the Dublin University seats. -
Maxwell and the Rings of Saturn
newsletter OF THE James Clerk Maxwell Foundation Issue No.5 Spring 2 015 Maxwell a nd t he Rings of Saturn by Professor Andrew Whitaker, Emeritus Professor of Physics, Queen’s University, Belfast Le Verrier, or to be worthy of the credit bestowed on him by Britain and, in particular, Cambridge. The funds for the Adams Prize were A view of the rings of Saturn (from Gribbin, John and provided by alumni of Adams’ Cambridge Goodwin, Simon (1998). Empire of the Sun: Planets college, St. John’s, and the prize was in and Moons of the Solar System. Constable, London.) the gift of the University. Airy and Challis were heavily involved in choosing topics Maxwell considered the rings of Saturn Against this background, why was in the first few years of the prize, and in to be ‘ the most remarkable bodies in the Maxwell prepared to put in so much work Maxwell’s year William Thomson was heavens ’, second only, in his opinion, to over several years on the rings of Saturn? also an examiner. Thomson, later Lord the spiral nebulae. Yet it seems extremely Admittedly the prize was substantial – Kelvin, had, of course, been Professor of unlikely that he would have devoted £130, or perhaps £13,000 in today’s terms, Natural Philosophy at Glasgow University a substantial amount of time and and this was rather more than a third of since 1846, but retained very strong links effort to determining their structure his full year’s salary at Aberdeen. But it is with Cambridge throughout his career. mathematically had the topic not been more likely that the reasons for taking Thus the institution of the Adams Prize chosen in 1855 as the subject of the on the challenge were, firstly, personal and the quality of the prize-winning Adams Prize of 1856. -
Lesson 2: the Multiplication of Polynomials
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 2 M1 ALGEBRA II Lesson 2: The Multiplication of Polynomials Student Outcomes . Students develop the distributive property for application to polynomial multiplication. Students connect multiplication of polynomials with multiplication of multi-digit integers. Lesson Notes This lesson begins to address standards A-SSE.A.2 and A-APR.C.4 directly and provides opportunities for students to practice MP.7 and MP.8. The work is scaffolded to allow students to discern patterns in repeated calculations, leading to some general polynomial identities that are explored further in the remaining lessons of this module. As in the last lesson, if students struggle with this lesson, they may need to review concepts covered in previous grades, such as: The connection between area properties and the distributive property: Grade 7, Module 6, Lesson 21. Introduction to the table method of multiplying polynomials: Algebra I, Module 1, Lesson 9. Multiplying polynomials (in the context of quadratics): Algebra I, Module 4, Lessons 1 and 2. Since division is the inverse operation of multiplication, it is important to make sure that your students understand how to multiply polynomials before moving on to division of polynomials in Lesson 3 of this module. In Lesson 3, division is explored using the reverse tabular method, so it is important for students to work through the table diagrams in this lesson to prepare them for the upcoming work. There continues to be a sharp distinction in this curriculum between justification and proof, such as justifying the identity (푎 + 푏)2 = 푎2 + 2푎푏 + 푏 using area properties and proving the identity using the distributive property. -
The Cambridge Mathematical Journal and Its Descendants: the Linchpin of a Research Community in the Early and Mid-Victorian Age ✩
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Historia Mathematica 31 (2004) 455–497 www.elsevier.com/locate/hm The Cambridge Mathematical Journal and its descendants: the linchpin of a research community in the early and mid-Victorian Age ✩ Tony Crilly ∗ Middlesex University Business School, Hendon, London NW4 4BT, UK Received 29 October 2002; revised 12 November 2003; accepted 8 March 2004 Abstract The Cambridge Mathematical Journal and its successors, the Cambridge and Dublin Mathematical Journal,and the Quarterly Journal of Pure and Applied Mathematics, were a vital link in the establishment of a research ethos in British mathematics in the period 1837–1870. From the beginning, the tension between academic objectives and economic viability shaped the often precarious existence of this line of communication between practitioners. Utilizing archival material, this paper presents episodes in the setting up and maintenance of these journals during their formative years. 2004 Elsevier Inc. All rights reserved. Résumé Dans la période 1837–1870, le Cambridge Mathematical Journal et les revues qui lui ont succédé, le Cambridge and Dublin Mathematical Journal et le Quarterly Journal of Pure and Applied Mathematics, ont joué un rôle essentiel pour promouvoir une culture de recherche dans les mathématiques britanniques. Dès le début, la tension entre les objectifs intellectuels et la rentabilité économique marqua l’existence, souvent précaire, de ce moyen de communication entre professionnels. Sur la base de documents d’archives, cet article présente les épisodes importants dans la création et l’existence de ces revues. 2004 Elsevier Inc. -
Act Mathematics
ACT MATHEMATICS Improving College Admission Test Scores Contributing Writers Marie Haisan L. Ramadeen Matthew Miktus David Hoffman ACT is a registered trademark of ACT Inc. Copyright 2004 by Instructivision, Inc., revised 2006, 2009, 2011, 2014 ISBN 973-156749-774-8 Printed in Canada. All rights reserved. No part of the material protected by this copyright may be reproduced in any form or by any means, for commercial or educational use, without permission in writing from the copyright owner. Requests for permission to make copies of any part of the work should be mailed to Copyright Permissions, Instructivision, Inc., P.O. Box 2004, Pine Brook, NJ 07058. Instructivision, Inc., P.O. Box 2004, Pine Brook, NJ 07058 Telephone 973-575-9992 or 888-551-5144; fax 973-575-9134, website: www.instructivision.com ii TABLE OF CONTENTS Introduction iv Glossary of Terms vi Summary of Formulas, Properties, and Laws xvi Practice Test A 1 Practice Test B 16 Practice Test C 33 Pre Algebra Skill Builder One 51 Skill Builder Two 57 Skill Builder Three 65 Elementary Algebra Skill Builder Four 71 Skill Builder Five 77 Skill Builder Six 84 Intermediate Algebra Skill Builder Seven 88 Skill Builder Eight 97 Coordinate Geometry Skill Builder Nine 105 Skill Builder Ten 112 Plane Geometry Skill Builder Eleven 123 Skill Builder Twelve 133 Skill Builder Thirteen 145 Trigonometry Skill Builder Fourteen 158 Answer Forms 165 iii INTRODUCTION The American College Testing Program Glossary: The glossary defines commonly used (ACT) is a comprehensive system of data mathematical expressions and many special and collection, processing, and reporting designed to technical words. -
Electrophonic Musical Instruments
G10H CPC COOPERATIVE PATENT CLASSIFICATION G PHYSICS (NOTES omitted) INSTRUMENTS G10 MUSICAL INSTRUMENTS; ACOUSTICS (NOTES omitted) G10H ELECTROPHONIC MUSICAL INSTRUMENTS (electronic circuits in general H03) NOTE This subclass covers musical instruments in which individual notes are constituted as electric oscillations under the control of a performer and the oscillations are converted to sound-vibrations by a loud-speaker or equivalent instrument. WARNING In this subclass non-limiting references (in the sense of paragraph 39 of the Guide to the IPC) may still be displayed in the scheme. 1/00 Details of electrophonic musical instruments 1/053 . during execution only {(voice controlled (keyboards applicable also to other musical instruments G10H 5/005)} instruments G10B, G10C; arrangements for producing 1/0535 . {by switches incorporating a mechanical a reverberation or echo sound G10K 15/08) vibrator, the envelope of the mechanical 1/0008 . {Associated control or indicating means (teaching vibration being used as modulating signal} of music per se G09B 15/00)} 1/055 . by switches with variable impedance 1/0016 . {Means for indicating which keys, frets or strings elements are to be actuated, e.g. using lights or leds} 1/0551 . {using variable capacitors} 1/0025 . {Automatic or semi-automatic music 1/0553 . {using optical or light-responsive means} composition, e.g. producing random music, 1/0555 . {using magnetic or electromagnetic applying rules from music theory or modifying a means} musical piece (automatically producing a series of 1/0556 . {using piezo-electric means} tones G10H 1/26)} 1/0558 . {using variable resistors} 1/0033 . {Recording/reproducing or transmission of 1/057 . by envelope-forming circuits music for electrophonic musical instruments (of 1/0575 . -
William Robertson Smith, Solomon Schechter and Contemporary Judaism
https://doi.org/10.14324/111.444.jhs.2016v48.026 William Robertson Smith, Solomon Schechter and contemporary Judaism bernhard maier University of Tübingen, Germany* During Solomon Schechter’s first years in the University of Cambridge, one of his most illustrious colleagues was the Scottish Old Testament scholar and Arabist William Robertson Smith (1846–1894), who is today considered to be among the founding fathers of comparative religious studies. Smith was the son of a minister of the strongly evangelical Free Church of Scotland, which had constituted itself in 1843 as a rival to the state-controlled established Church of Scotland. Appointed Professor of Old Testament Exegesis in the Free Church College Aberdeen at the early age of twenty-four, Smith soon came into conflict with the conservative theologians of his church on account of his critical views. After a prolonged heresy trial, he was finally deprived of his Aberdeen chair in 1881. In 1883 he moved to Cambridge, where he served, successively, as Lord Almoner’s Reader in Arabic, University Librarian, and Thomas Adams’s Professor of Arabic. Discussing Schechter’s relations with Robertson Smith, one has to bear in mind that direct contact between Schechter and Smith was confined to a relatively short period of less than five years (1890–94), during which Smith was frequently ill and consequently not resident in Cambridge at all.1 Furthermore, there is not much written evidence, so that several hints and clues that have come down to us are difficult to interpret, our understanding being sometimes based on inference and reasoning by analogy rather than on any certain knowledge. -
Hydrodynamic Instabilities in Laser Produced Plasmas
the united nations educational, scientific abdus salam and cultural organization international centre for theoretical physics international atomic energy agency SMR 1521/17 AUTUMN COLLEGE ON PLASMA PHYSICS 13 October - 7 November 2003 Hydrodynamic Instabilities in Laser Produced Plasmas S. Atzeni Universita' "La Sapienza" and INFM Roma, Italy These are preliminary lecture notes, intended only for distribution to participants. strada costiera, I I - 34014 trieste italy - tel.+39 040 22401 I I fax+39 040 224163 - [email protected] -www.ictp.trieste.it UNIVERSITA' DEGLI STUDI DI ROMA LA SAPIENZA DIPARTIMENTO DI ENERGETICA Hydrodynamic Instabilities in Laser Produced Plasmas Stefano Atzeni Dipartimento di Energetica Universita di Roma "La Sapienza" and INFM Via A. Scarpa, 14-16, 00161 Roma, Italy E-mail: [email protected] Autumn College on Plasma Physics The Abdus Salam International Centre for Theoretical Physics Trieste, 13 October - 7 November 2003 The following material is Chapter 8 of the book "Physics of inertial confinement fusion" by S. Atzeni and J. Meyer-ter-Vehn Clarendon Press, Oxford (to appear in Spring 2004) -io Ok) 8 HYDRODYNAMIC STABILITY This chapter is devoted to hydrodynamic instabilities. ICF capsule implosions are inherently unstable. In particular, the Rayleigh-Taylor instability (RTI) tends to destroy the imploding shell (see Fig. 8.1). It should be clear that the goal of central hot spot ignition depends most critically on how to control the instability. Fig. 8.1 This is a major challenge facing ICF. For this reason, large efforts have been undertaken over the last two decades to study all aspects of RTI and related instabilities. -
Orientalism As Represented in the Selected Piano Works by Claude Debussy
Chapter 4 ORIENTALISM AS REPRESENTED IN THE SELECTED PIANO WORKS BY CLAUDE DEBUSSY A prominent English scholar of French music, Roy Howat, claimed that, out of the many composers who were attracted by the Orient as subject matter, “Debussy is the one who made much of it his own language, even identity.”55 Debussy and Hahn, despite being in the same social circle, never pursued an amicable relationship.56 Even while keeping their distance, both composers were somewhat aware of the other’s career. Hahn, in a public statement from 1890, praised highly Debussy’s musical artistry in L'Apres- midi d'un faune.57 Debussy’s Exposure to Oriental Cultures Debussy’s first exposure to oriental art and philosophy began at Mallarmé’s Symbolist gatherings he frequented in 1887 upon his return to Paris from Rome.58 At the Universal Exposition of 1889, he had his first experience in the theater of Annam (Vietnam) and the Javanese Gamelan orchestra (Indonesia), which is said to be a catalyst 55Roy Howat, The Art of French Piano Music: Debussy, Ravel, Fauré, Chabrier (New Haven, Conn.: Yale University Press, 2009), 110 56Gavoty, 142. 57Ibid., 146. 58François Lesure and Roy Howat. "Debussy, Claude." In Grove Music Online. Oxford Music Online, http://www.oxfordmusiconline.com/subscriber/article/grove/music/07353 (accessed April 4, 2011). 33 34 in his artistic direction. 59 In 1890, Debussy was acquainted with Edmond Bailly, esoteric and oriental scholar, who took part in publishing and selling some of Debussy’s music at his bookstore L’Art Indépendeant. 60 In 1902, Debussy met Louis Laloy, an ethnomusicologist and music critic who eventually became Debussy’s most trusted friend and encouraged his use of Oriental themes.61 After the Universal Exposition in 1889, Debussy had another opportunity to listen to a Gamelan orchestra 11 years later in 1900. -
Convective to Absolute Instability Transition in a Horizontal Porous Channel with Open Upper Boundary
fluids Article Convective to Absolute Instability Transition in a Horizontal Porous Channel with Open Upper Boundary Antonio Barletta * and Michele Celli Department of Industrial Engineering, Alma Mater Studiorum Università di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy; [email protected] * Correspondence: [email protected]; Tel.: +39-051-209-3287 Academic Editor: Mehrdad Massoudi Received: 28 April 2017; Accepted: 10 June 2017; Published: 14 June 2017 Abstract: A linear stability analysis of the parallel uniform flow in a horizontal channel with open upper boundary is carried out. The lower boundary is considered as an impermeable isothermal wall, while the open upper boundary is subject to a uniform heat flux and it is exposed to an external horizontal fluid stream driving the flow. An eigenvalue problem is obtained for the two-dimensional transverse modes of perturbation. The study of the analytical dispersion relation leads to the conditions for the onset of convective instability as well as to the determination of the parametric threshold for the transition to absolute instability. The results are generalised to the case of three-dimensional perturbations. Keywords: porous medium; Rayleigh number; absolute instability 1. Introduction Cellular convection patterns may develop in an underlying horizontal flow under appropriate thermal boundary conditions. The classic setup for the thermal instability of a horizontal fluid flow is heating from below, and the well-known type of instability is Rayleigh-Bénard [1]. Such a situation can happen in a channel fluid flow or in the filtration of a fluid within a porous channel. Both cases are widely documented in the literature [1,2]. -
Blue Plaque Guide
Blue Plaque Guide Research and Cultural Collections 2 Blue Plaque Guide Foreword 3 Introduction 4 1 Dame Hilda Lloyd 6 2 Leon Abrams and Ray Lightwood 7 3 Sir Norman Haworth 8 4 Sir Peter Medawar 9 5 Charles Lapworth 10 6 Frederick Shotton 11 7 Sir Edward Elgar 12 8 Sir Granville Bantock 13 9 Otto Robert Frisch and Sir Rudolf E Peierls 14 10 John Randall and Harry Boot 15 11 Sir Mark Oliphant 16 12 John Henry Poynting 17 13 Margery Fry 18 14 Sir William Ashley 19 15 George Neville Watson 20 16 Louis MacNeice 21 17 Sir Nikolaus Pevsner 22 18 David Lodge 23 19 Francois Lafi tte 24 20 The Centre for Contemporary Cultural Studies 25 21 John Sutton Nettlefold 26 22 John Sinclair 27 23 Marie Corelli 28 Acknowledgments 29 Visit us 30 Map 31 Blue Plaque Guide 3 Foreword Across the main entrance to the Aston Webb Building, the historic centre of our campus, is a line of standing male figures carved into the fabric by Henry Pegram. If this were a cathedral, they would be saints or prophets; changed the world, from their common home the University but this is the University of Birmingham, and the people of Birmingham. who greet us as we pass through those doors are Beethoven, Virgil, Michelangelo, Plato, Shakespeare, The University’s Research and Cultural Collections, Newton, Watt, Faraday and Darwin. While only one of working with Special Collections, the Lapworth Museum, those (Shakespeare) was a local lad, and another (Watt) the Barber Institute of Fine Arts and Winterbourne House local by adoption, together they stand for the primacy of and Garden, reflect the cross-disciplinary nature of the creativity.