The Life of James Clerk Maxwell by Lewis Campbell and William Garnett
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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. -
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. -
James Clerk Maxwell
James Clerk Maxwell JAMES CLERK MAXWELL Perspectives on his Life and Work Edited by raymond flood mark mccartney and andrew whitaker 3 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries c Oxford University Press 2014 The moral rights of the authors have been asserted First Edition published in 2014 Impression: 1 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, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2013942195 ISBN 978–0–19–966437–5 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. -
Philosophical Transactions, »
INDEX TO THE PHILOSOPHICAL TRANSACTIONS, » S e r ie s A, FOR THE YEAR 1898 (VOL. 191). A. Absorption, Change of, produced by Fluorescence (B urke), 87. Aneroid Barometers, Experiments on.—Elastic After-effect; Secular Change; Influence of Temperature (Chree), 441. B. Bolometer, Surface, Construction of (Petavel), 501. Brilliancy, Intrinsic, Law of Variation of, with Temperature (Petavel), 501. Burke (John). On the Change of Absorption produced by Fluorescence, 87. C. Chree (C.). Experiments on Aneroid Barometers at Kew Observatory, and their Discussion, 441. Correlation and Variation, Influence of Random Selection on (Pearson and Filon), 229. Crystals, Thermal Expansion Coefficients, by an Interference Method (Tutton), 313. D. Differential Equations of the Second Order, &c., Memoir on the Integration of; Characteristic Invariant of (Forsyth), 1. 526 INDEX. E. Electric Filters, Testing Efficiency of; Dielectrifying Power of (Kelvin, Maclean, and Galt), 187. Electricity, Diffusion of, from Carbonic Acid Gas to Air; Communication of, from Electrified Steam to Air (Kelvin, Maclean, and Galt), 187. Electrification of Air by Water Jet, Electrified Needle Points, Electrified Flame, &c., at Different Air-pressures; at Different Electrifying Potentials; Loss of Electrification (Kelvin, Maclean, and Galt), 187. Electrolytic Cells, Construction and Calibration of (Veley and Manley), 365. Emissivity of Platinum in Air and other Gases (Petavel), 501. Equations, Laplace's and other, Some New Solutions of, in Mathematical Physics (Forsyth), 1. Evolution, Mathematical Contributions to Theory o f; Influence of Random Selection on the Differentiation of Local Races (Pearson and Filon), 229. F. Filon (L. N. G.) and Pearson (Karl). Mathematical Contributions to the Theory of Evolution.—IV. On the Probable Errors of Frequency Constants and on the Influence of Random Selection on Variation and Correlation, 229. -
Combination of Cubic and Quartic Plane Curve
IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728,p-ISSN: 2319-765X, Volume 6, Issue 2 (Mar. - Apr. 2013), PP 43-53 www.iosrjournals.org Combination of Cubic and Quartic Plane Curve C.Dayanithi Research Scholar, Cmj University, Megalaya Abstract The set of complex eigenvalues of unistochastic matrices of order three forms a deltoid. A cross-section of the set of unistochastic matrices of order three forms a deltoid. The set of possible traces of unitary matrices belonging to the group SU(3) forms a deltoid. The intersection of two deltoids parametrizes a family of Complex Hadamard matrices of order six. The set of all Simson lines of given triangle, form an envelope in the shape of a deltoid. This is known as the Steiner deltoid or Steiner's hypocycloid after Jakob Steiner who described the shape and symmetry of the curve in 1856. The envelope of the area bisectors of a triangle is a deltoid (in the broader sense defined above) with vertices at the midpoints of the medians. The sides of the deltoid are arcs of hyperbolas that are asymptotic to the triangle's sides. I. Introduction Various combinations of coefficients in the above equation give rise to various important families of curves as listed below. 1. Bicorn curve 2. Klein quartic 3. Bullet-nose curve 4. Lemniscate of Bernoulli 5. Cartesian oval 6. Lemniscate of Gerono 7. Cassini oval 8. Lüroth quartic 9. Deltoid curve 10. Spiric section 11. Hippopede 12. Toric section 13. Kampyle of Eudoxus 14. Trott curve II. Bicorn curve In geometry, the bicorn, also known as a cocked hat curve due to its resemblance to a bicorne, is a rational quartic curve defined by the equation It has two cusps and is symmetric about the y-axis. -
Dissertation Revision
Harmonic Centricity in Philip Glass’ “The Grid” and “Cowboy Rock’n’Roll USA,” an original composition by Matthew Donald Aelmore B.M., Wichita State University, 2009 M.M., Manhattan School of Music, 2011 Submitted to the Graduate Faculty of the Dietrich School of Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Music Composition and Theory University of Pittsburgh 2015 UNIVERSITY OF PITTSBURGH Dietrich School of Arts and Sciences This dissertation was presented by Matthew Donald Aelmore It was defended on March 26, 2015 and approved by Marcia Landy, PhD, Professor of English/Film Studies Eric Moe, PhD, Professor of Music Composition and Theory Andrew Weintraub, PhD, Professor of Ethnomusicology Dissertation Advisor: Amy Williams, PhD, Professor of Music Composition and Theory ii Harmonic Centricity in Philip Glass’ “The Grid” and “Cowboy Rock’n’Roll USA,” an original composition Matthew Donald Aelmore, PhD University of Pittsburgh, 2015 Copyright © by Matthew Donald Aelmore 2015 iii Harmonic Centricity in Philip Glass’ “The Grid” and “Cowboy Rock’n’Roll USA,” an original composition Matthew Aelmore, PhD University of Pittsburgh, 2015 This dissertation analyzes the harmonic syntax of Philip Glass’ music for the scene “The Grid,” from the 1982 Godfrey Reggio film Koyaanisqatsi. Chapter 1 focuses on the five harmonic cycles, which are presented in twenty-one harmonic sections. Due to the effects of repetition, Glass’ harmonic cycles are satiated from the relationships of consonance and dissonance that characterize tonal harmony. The five harmonic cycles, which appear in twenty-one sections, are analyzed in terms of the type of harmonic centricity they assert: tonally harmonic centricity, contextually asserted harmonic centricity, and no harmonic centricity. -
Using Elimination to Describe Maxwell Curves Lucas P
Louisiana State University LSU Digital Commons LSU Master's Theses Graduate School 2006 Using elimination to describe Maxwell curves Lucas P. Beverlin Louisiana State University and Agricultural and Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_theses Part of the Applied Mathematics Commons Recommended Citation Beverlin, Lucas P., "Using elimination to describe Maxwell curves" (2006). LSU Master's Theses. 2879. https://digitalcommons.lsu.edu/gradschool_theses/2879 This Thesis is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Master's Theses by an authorized graduate school editor of LSU Digital Commons. For more information, please contact [email protected]. USING ELIMINATION TO DESCRIBE MAXWELL CURVES A Thesis Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial ful¯llment of the requirements for the degree of Master of Science in The Department of Mathematics by Lucas Paul Beverlin B.S., Rose-Hulman Institute of Technology, 2002 August 2006 Acknowledgments This dissertation would not be possible without several contributions. I would like to thank my thesis advisor Dr. James Madden for his many suggestions and his patience. I would also like to thank my other committee members Dr. Robert Perlis and Dr. Stephen Shipman for their help. I would like to thank my committee in the Experimental Statistics department for their understanding while I completed this project. And ¯nally I would like to thank my family for giving me the chance to achieve a higher education. -
Statutes and Rules for the British Museum
(ft .-3, (*y Of A 8RI A- \ Natural History Museum Library STATUTES AND RULES BRITISH MUSEUM STATUTES AND RULES FOR THE BRITISH MUSEUM MADE BY THE TRUSTEES In Pursuance of the Act of Incorporation 26 George II., Cap. 22, § xv. r 10th Decembei , 1898. PRINTED BY ORDER OE THE TRUSTEES LONDON : MDCCCXCYIII. PRINTED BY WOODFALL AND KINDER, LONG ACRE LONDON TABLE OF CONTENTS CHAPTER I. PAGE Meetings, Functions, and Privileges of the Trustees . 7 CHAPTER II. The Director and Principal Librarian . .10 Duties as Secretary and Accountant . .12 The Director of the Natural History Departments . 14 CHAPTER III. Subordinate Officers : Keepers and Assistant Keepers 15 Superintendent of the Reading Room . .17 Assistants . 17 Chief Messengers . .18 Attendance of Officers at Meetings, etc. -19 CHAPTER IV. Admission to the British Museum : Reading Room 20 Use of the Collections 21 6 CHAPTER V, Security of the Museum : Precautions against Fire, etc. APPENDIX. Succession of Trustees and Officers . Succession of Officers in Departments 7 STATUTES AND RULES. CHAPTER I. Of the Meetings, Functions, and Privileges of the Trustees. 1. General Meetings of the Trustees shall chap. r. be held four times in the year ; on the second Meetings. Saturday in May and December at the Museum (Bloomsbury) and on the fourth Saturday in February and July at the Museum (Natural History). 2. Special General Meetings shall be sum- moned by the Director and Principal Librarian (hereinafter called the Director), upon receiving notice in writing to that effect signed by two Trustees. 3. There shall be a Standing Committee, standing . • Committee. r 1 1 t-» • 1 t> 1 consisting 01 the three Principal 1 rustees, the Trustee appointed by the Crown, and sixteen other Trustees to be annually appointed at the General Meeting held on the second Saturday in May. -
Middlesex University Research Repository
Middlesex University Research Repository An open access repository of Middlesex University research http://eprints.mdx.ac.uk Delve, Janet (1999) The development of the mathematical department of the Educational Times from 1847 to 1862. PhD thesis, Middlesex University. Available from Middlesex University’s Research Repository at http://eprints.mdx.ac.uk/7993/ Copyright: Middlesex University Research Repository makes the University’s research available electronically. Copyright and moral rights to this thesis/research project are retained by the author and/or other copyright owners. The work is supplied on the understanding that any use for commercial gain is strictly forbidden. A copy may be downloaded for personal, non- commercial, research or study without prior permission and without charge. Any use of the thesis/research project for private study or research must be properly acknowledged with reference to the work’s full bibliographic details. This thesis/research project may not be reproduced in any format or medium, or extensive quotations taken from it, or its content changed in any way, without first obtaining permission in writing from the copyright holder(s). If you believe that any material held in the repository infringes copyright law, please contact the Repository Team at Middlesex University via the following email address: [email protected] The item will be removed from the repository while any claim is being investigated. MX 7226926 X Contents ABSTRACT Mathematics held an important place in the first twelve of years of the Educational Times (1847-1923), and in November 1848 a department of mathematical questions and solutions was launched. In 1864 this department was reprinted in a daughter journal: Mathematical Questions with Their solutions from The Educational Times (MQ). -
A Beautiful Approach: Transformational Optics
A beautiful approach: “Transformational optics” [ several precursors, but generalized & popularized by Ward & Pendry (1996) ] warp a ray of light …by warping space(?) [ figure: J. Pendry ] Euclidean x coordinates transformed x'(x) coordinates amazing Solutions of ordinary Euclidean Maxwell equations in x' fact: = transformed solutions from x if x' uses transformed materials ε' and μ' Maxwell’s Equations constants: ε0, μ0 = vacuum permittivity/permeability = 1 –1/2 c = vacuum speed of light = (ε0 μ0 ) = 1 ! " B = 0 Gauss: constitutive ! " D = # relations: James Clerk Maxwell #D E = D – P 1864 Ampere: ! " H = + J #t H = B – M $B Faraday: ! " E = # $t electromagnetic fields: sources: J = current density E = electric field ρ = charge density D = displacement field H = magnetic field / induction material response to fields: B = magnetic field / flux density P = polarization density M = magnetization density Constitutive relations for macroscopic linear materials P = χe E ⇒ D = (1+χe) E = ε E M = χm H B = (1+χm) H = μ H where ε = 1+χe = electric permittivity or dielectric constant µ = 1+χm = magnetic permeability εµ = (refractive index)2 Transformation-mimicking materials [ Ward & Pendry (1996) ] E(x), H(x) J–TE(x(x')), J–TH(x(x')) [ figure: J. Pendry ] Euclidean x coordinates transformed x'(x) coordinates J"JT JµJT ε(x), μ(x) " ! = , µ ! = (linear materials) det J det J J = Jacobian (Jij = ∂xi’/∂xj) (isotropic, nonmagnetic [μ=1], homogeneous materials ⇒ anisotropic, magnetic, inhomogeneous materials) an elementary derivation [ Kottke (2008) ] consider× -
History Unveiling Prophecy (Or Time As an Interpreter)
1906 Digitally formatted for Historicism.com in 2003 courtesy of B. Keenan. "Reading The Approaching End of the Age was somewhat of a turning point in my belief in the bible. It is a very convincing argument that the bible is influenced by some supernatural power. It has given me a strong enthusiasm for learning more of what H. Grattan Guinness has to say, along with many other authors that cover end time (current) events, and the plethora of fabricated events in history leading to this stage." – B. Keenan For more information on Henry Grattan Guinness, and a list of his works that are available on the Internet, visit the H. Grattan Guinness Archive at http://www.historicism.com/Guinness. © 2003 Historicism.com PREFACE THE lofty decree of Papal Infallibility issued by the Vatican Council of 1870, immediately followed by the sudden and final fall of the Papal Temporal Power, after a duration of more than a thousand years, was the primary occasion of my writing that series of works on the fulfilment of Scripture prophecy which has appeared during the last quarter of a century. I left Paris, where I had been labouring in the Gospel, at the outbreak of the Franco-German war in July, 1870. It was in the light of the German bombardment of that city, of the ring of fire which surrounded it, and of the burning of the Tuileries, that I began to read with interest and understanding the prophecies of Daniel and the Apocalypse. Subsequent visits to Italy and Rome enlarged my view of the subject. -
Advance Program Notes Powaqqatsi: Life in Transformation Philip Glass Ensemble Friday, November 1, 2013, 8 PM
Advance Program Notes Powaqqatsi: Life in Transformation Philip Glass Ensemble Friday, November 1, 2013, 8 PM These Advance Program Notes are provided online for our patrons who like to read about performances ahead of time. Printed programs will be provided to patrons at the performances. Programs are subject to change. CENTER FOR THE ARTS AT VIRGINIA TECH presents POWAQQATSI LIFE IN TRANSFORMATION The CANNON GROUP INC. A FRANCIS FORD COPPOLA and GEORGE LUCAS Presentation Music by Directed by PHILIP GLASS GODFREY REGGIO Photography by Edited by GRAHAM BERRY IRIS CAHN/ ALTON WALPOLE LEONIDAS ZOURDOUMIS Performed by PHILIP GLASS and the PHILIP GLASS ENSEMBLE conducted by Michael Riesman with the Blacksburg Children’s Chorale Patrice Yearwood, artistic director PHILIP GLASS ENSEMBLE Philip Glass, Lisa Bielawa, Dan Dryden, Stephen Erb, Jon Gibson, Michael Riesman, Mick Rossi, Andrew Sterman, David Crowell Guest Musicians: Ted Baker, Frank Cassara, Nelson Padgett, Yousif Sheronick The call to prayer in tonight’s performance is given by Dr. Khaled Gad Music Director MICHAEL RIESMAN Sound Design by Kurt Munkacsi Film Executive Producers MENAHEM GOLAN and YORAM GLOBUS Film Produced by MEL LAWRENCE, GODFREY REGGIO and LAWRENCE TAUB Production Management POMEGRANATE ARTS Linda Brumbach, Producer POWAQQATSI runs approximately 102 minutes and will be performed without intermission. SUBJECT TO CHANGE PO-WAQ-QA-TSI (from the Hopi language, powaq sorcerer + qatsi life) n. an entity, a way of life, that consumes the life forces of other beings in order to further its own life. POWAQQATSI is the second part of the Godfrey Reggio/Philip Glass QATSI TRILOGY. With a more global view than KOYAANISQATSI, Reggio and Glass’ first collaboration, POWAQQATSI, examines life on our planet, focusing on the negative transformation of land-based, human- scale societies into technologically driven, urban clones.