COURSE STRUCTURE and DETAILED SYLLABUS (MR14 Regulations)
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Polar Coordinates and Complex Numbers Infinite Series Vectors and Matrices Motion Along a Curve Partial Derivatives
Contents CHAPTER 9 Polar Coordinates and Complex Numbers 9.1 Polar Coordinates 348 9.2 Polar Equations and Graphs 351 9.3 Slope, Length, and Area for Polar Curves 356 9.4 Complex Numbers 360 CHAPTER 10 Infinite Series 10.1 The Geometric Series 10.2 Convergence Tests: Positive Series 10.3 Convergence Tests: All Series 10.4 The Taylor Series for ex, sin x, and cos x 10.5 Power Series CHAPTER 11 Vectors and Matrices 11.1 Vectors and Dot Products 11.2 Planes and Projections 11.3 Cross Products and Determinants 11.4 Matrices and Linear Equations 11.5 Linear Algebra in Three Dimensions CHAPTER 12 Motion along a Curve 12.1 The Position Vector 446 12.2 Plane Motion: Projectiles and Cycloids 453 12.3 Tangent Vector and Normal Vector 459 12.4 Polar Coordinates and Planetary Motion 464 CHAPTER 13 Partial Derivatives 13.1 Surfaces and Level Curves 472 13.2 Partial Derivatives 475 13.3 Tangent Planes and Linear Approximations 480 13.4 Directional Derivatives and Gradients 490 13.5 The Chain Rule 497 13.6 Maxima, Minima, and Saddle Points 504 13.7 Constraints and Lagrange Multipliers 514 CHAPTER 12 Motion Along a Curve I [ 12.1 The Position Vector I-, This chapter is about "vector functions." The vector 2i +4j + 8k is constant. The vector R(t) = ti + t2j+ t3k is moving. It is a function of the parameter t, which often represents time. At each time t, the position vector R(t) locates the moving body: position vector =R(t) =x(t)i + y(t)j + z(t)k. -
The Stannaries
THE STANNARIES A STUDY OF THE MEDIEVAL TIN MINERS OF CORNWALL AND DEVON G. R. LEWIS First published 1908 PREFACE THEfollowing monograph, the outcome of a thesis for an under- graduate course at Harvard University, is the result of three years' investigation, one in this country and two in England, - for the most part in London, where nearly all the documentary material relating to the subject is to be found. For facilitating with ready courtesy my access to this material I am greatly indebted to the officials of the 0 GEORGE RANDALL LEWIS British Museum, the Public Record Office, and the Duchy of Corn- wall Office. I desire also to acknowledge gratefully the assistance of Dr. G. W. Prothero, Mr. Hubert Hall, and Mr. George Unwin. My thanks are especially due to Professor Edwin F. Gay of Harvard University, under whose supervision my work has been done. HOUGHTON,M~CHIGAN, November, 1907. CONTENTS INTRODUCTION purpose of the essay. Reasons for choice of subject. Sources of informa- tion. Plan of treatment . xiii CHAPTER I Nature of tin ore. Stream tinning in early times. Early methods of searching for ore. Forms assumed by the primitive mines. Drainage and other features of medizval mine economy. Preparation of the ore. Carew's description of the dressing of tin ore. Early smelting furnaces. Advances in mining and smelt- ing in the latter half of the seventeenth century. Preparation of the ore. Use of the steam engine for draining mines. Introduction of blasting. Pit coal smelting. General advance in ore dressing in the eighteenth century. Other improvements. -
Arts Revealed in Calculus and Its Extension
See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/265557431 Arts revealed in calculus and its extension Article · August 2014 CITATIONS READS 9 455 1 author: Hanna Arini Parhusip Universitas Kristen Satya Wacana 95 PUBLICATIONS 89 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Pusnas 2015/2016 View project All content following this page was uploaded by Hanna Arini Parhusip on 16 September 2014. The user has requested enhancement of the downloaded file. [Type[Type aa quotequote fromfrom thethe documentdocument oror thethe International Journal of Statistics and Mathematics summarysummary ofof anan interestinginteresting point.point. YouYou cancan Vol. 1(3), pp. 016-023, August, 2014. © www.premierpublishers.org, ISSN: xxxx-xxxx x positionposition thethe texttext boxbox anywhereanywhere inin thethe IJSM document. Use the Text Box Tools tab to document. Use the Text Box Tools tab to changechange thethe formattingformatting ofof thethe pullpull quotequote texttext box.]box.] Review Arts revealed in calculus and its extension Hanna Arini Parhusip Mathematics Department, Science and Mathematics Faculty, Satya Wacana Christian University (SWCU)-Jl. Diponegoro 52-60 Salatiga, Indonesia Email: [email protected], Tel.:0062-298-321212, Fax: 0062-298-321433 Motivated by presenting mathematics visually and interestingly to common people based on calculus and its extension, parametric curves are explored here to have two and three dimensional objects such that these objects can be used for demonstrating mathematics. Epicycloid, hypocycloid are particular curves that are implemented in MATLAB programs and the motifs are presented here. The obtained curves are considered to be domains for complex mappings to have new variation of Figures and objects. -
Cc21-102 Addendum #2 Bear Valley Road
Kris J. Kofoed From: Sanchez, Jason L <[email protected]> Sent: Monday, June 14, 2021 1:27 PM To: Jamie Formico Cc: Kris J. Kofoed; Townlian, Cheryl L Subject: FW: City of Victorville- Bear Valley out to Bid Attachments: C&M Agreement.pdf; Pages from C&M Agreement (Executed).pdf; Pages from IIPlans.pdf CAUTION: This email originated from outside of the organization. Do not click links or open attachments unless you recognize the sender and know the content is safe. Hi Jamie: Per our recent conversation, the shoring system is 12 feet from the face to centerline of track. Even though this is less than the 15’ feet called out in C&M Agreement, this reduced clearance is only temporary (no more than 6 hours) and not an issue. During the construction of the shoring wall, a work window will be established to eliminate train traffic on the adjacent track for that short duration. Once installed, the shoring system will be at the same elevation or lower than the top of rail, making the 12 feet clearance moot. Any questions, please ask. Thank you, Jason L. Sanchez BNSF Railway Manager Engineering 740 E. Carnegie Drive San Bernardino, CA 92408 909-386-4470 [email protected] From: Jamie Formico <[email protected]> Sent: Wednesday, May 19, 2021 9:32 AM To: Sanchez, Jason L <[email protected]>; Townlian, Cheryl L <[email protected]>; Kris J. Kofoed <[email protected]> Subject: City of Victorville‐ Bear Valley out to Bid *** This email includes an ATTACHMENT from outside of BNSF and could contain malicious links. -
~ Coal Mining in Canada: a Historical and Comparative Overview
~ Coal Mining in Canada: A Historical and Comparative Overview Delphin A. Muise Robert G. McIntosh Transformation Series Collection Transformation "Transformation," an occasional paper series pub- La collection Transformation, publication en st~~rie du lished by the Collection and Research Branch of the Musee national des sciences et de la technologic parais- National Museum of Science and Technology, is intended sant irregulierement, a pour but de faire connaitre, le to make current research available as quickly and inex- plus vite possible et au moindre cout, les recherches en pensively as possible. The series presents original cours dans certains secteurs. Elle prend la forme de research on science and technology history and issues monographies ou de recueils de courtes etudes accep- in Canada through refereed monographs or collections tes par un comite d'experts et s'alignant sur le thenne cen- of shorter studies, consistent with the Corporate frame- tral de la Societe, v La transformation du CanadaLo . Elle work, "The Transformation of Canada," and curatorial presente les travaux de recherche originaux en histoire subject priorities in agricultural and forestry, communi- des sciences et de la technologic au Canada et, ques- cations and space, transportation, industry, physical tions connexes realises en fonction des priorites de la sciences and energy. Division de la conservation, dans les secteurs de: l'agri- The Transformation series provides access to research culture et des forets, des communications et de 1'cspace, undertaken by staff curators and researchers for develop- des transports, de 1'industrie, des sciences physiques ment of collections, exhibits and programs. Submissions et de 1'energie . -
On the Topology of Hypocycloid Curves
Física Teórica, Julio Abad, 1–16 (2008) ON THE TOPOLOGY OF HYPOCYCLOIDS Enrique Artal Bartolo∗ and José Ignacio Cogolludo Agustíny Departamento de Matemáticas, Facultad de Ciencias, IUMA Universidad de Zaragoza, 50009 Zaragoza, Spain Abstract. Algebraic geometry has many connections with physics: string theory, enu- merative geometry, and mirror symmetry, among others. In particular, within the topo- logical study of algebraic varieties physicists focus on aspects involving symmetry and non-commutativity. In this paper, we study a family of classical algebraic curves, the hypocycloids, which have links to physics via the bifurcation theory. The topology of some of these curves plays an important role in string theory [3] and also appears in Zariski’s foundational work [9]. We compute the fundamental groups of some of these curves and show that they are in fact Artin groups. Keywords: hypocycloid curve, cuspidal points, fundamental group. PACS classification: 02.40.-k; 02.40.Xx; 02.40.Re . 1. Introduction Hypocycloid curves have been studied since the Renaissance (apparently Dürer in 1525 de- scribed epitrochoids in general and then Roemer in 1674 and Bernoulli in 1691 focused on some particular hypocycloids, like the astroid, see [5]). Hypocycloids are described as the roulette traced by a point P attached to a circumference S of radius r rolling about the inside r 1 of a fixed circle C of radius R, such that 0 < ρ = R < 2 (see Figure 1). If the ratio ρ is rational, an algebraic curve is obtained. The simplest (non-trivial) hypocycloid is called the deltoid or the Steiner curve and has a history of its own both as a real and complex curve. -
Iii Year Course Structure & Syllabus (R16)
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.TECH. MINING ENGINEERING III YEAR COURSE STRUCTURE & SYLLABUS (R16) Applicable From 2016-17 Admitted Batch III YEAR I SEMESTER Course S. No Course Title L T P Credits Code 1 MN501PC Mine Environmental Engineering - II 4 1 0 4 2 MN502PC Underground Mining Technology 4 1 0 4 3 MN503PC Mine Mechanization - II 4 1 0 4 4 SM504MS Fundamentals of Management 3 0 0 3 5 Open Elective – I 3 0 0 3 6 MN505PC Mine Environmental Engineering - II Lab 0 0 3 2 7 MN506PC Mine Mechanization - II Lab 0 0 3 2 8 MN507PC Mine Surveying - II Lab 0 0 3 2 9 *MC500HS Professional Ethics 3 0 0 0 Total Credits 21 3 9 24 III YEAR II SEMESTER Course S. No Course Title L T P Credits Code 1 MN601PC Surface Mining Technology 4 1 0 4 2 MN602PC Mineral Process Engineering 4 1 0 4 3 MN603PC Rock Mechanics 4 1 0 4 4 Open Elective - II 3 0 0 3 5 Professional Elective - I 3 0 0 3 6 MN604PC Rock Mechanics Lab 0 0 3 2 7 MN605PC Mineral Processing Engineering Lab 0 0 3 2 8 EN606HS Advanced English Communication skills Lab 0 0 3 2 Total Credits 18 3 9 24 During Summer Vacation between III and IV Years: Industry Oriented Mini Project Professional Elective - I MN611PE Mine Systems Engineering MN612PE Remote Sensing and GIS in Mining MN613PE Dimensional Stone Technology MN614PE Mineral Exploration *Open Elective subjects’ syllabus is provided in a separate document. -
ABB's Long History of Making Mining Operations More Efficient
ABB’s long history of making mining operations more efficient Innovative technologies have improved productivity for mining since the 1890s ABB’s comprehensive automation and power delivery at Boliden’s Aitik copper concentrator plant is the latest chapter in the company’s rich history of improving the operations of all types of mines and ore processing plants. The company has provided solutions that make mining operations more efficient, productive and safe for almost 120 years, since delivering the first drives and controls for a mine hoist at the Kolningsberget iron mine in Norberg, Sweden, in 1891. Drives and controls help mine hoists operate more efficiently and consistently as they haul tons of ore from lower levels of a mine to the surface. Over the years, ABB has made other breakthroughs in mine hoist technology including hydraulic disc brakes, controlled braking and Rope Oscillation Control, all of which have made mine hoists more reliable and safer to operate. ABB has delivered more than 600 new hoists and modernized hundreds of existing plants. A mine hoist delivered around 1930 by ASEA, a predecessor of ABB, to the Zinkgruvan zinc mine in Sweden is still in operation today. Pioneer of gearless mill drives ABB pioneered the development of gearless mill drive (GMD) systems, which are giant motor and drive systems that power ore-crushing mills. They are more reliable and energy efficient than traditional mill drive systems, and increase mill productivity. ABB delivered the world’s first gearless machine drive to Lafarge Cement in France in 1969. The 6.4 megawatt (MW) equipment is still operating today. -
Around and Around ______
Andrew Glassner’s Notebook http://www.glassner.com Around and around ________________________________ Andrew verybody loves making pictures with a Spirograph. The result is a pretty, swirly design, like the pictures Glassner EThis wonderful toy was introduced in 1966 by Kenner in Figure 1. Products and is now manufactured and sold by Hasbro. I got to thinking about this toy recently, and wondered The basic idea is simplicity itself. The box contains what might happen if we used other shapes for the a collection of plastic gears of different sizes. Every pieces, rather than circles. I wrote a program that pro- gear has several holes drilled into it, each big enough duces Spirograph-like patterns using shapes built out of to accommodate a pen tip. The box also contains some Bezier curves. I’ll describe that later on, but let’s start by rings that have gear teeth on both their inner and looking at traditional Spirograph patterns. outer edges. To make a picture, you select a gear and set it snugly against one of the rings (either inside or Roulettes outside) so that the teeth are engaged. Put a pen into Spirograph produces planar curves that are known as one of the holes, and start going around and around. roulettes. A roulette is defined by Lawrence this way: “If a curve C1 rolls, without slipping, along another fixed curve C2, any fixed point P attached to C1 describes a roulette” (see the “Further Reading” sidebar for this and other references). The word trochoid is a synonym for roulette. From here on, I’ll refer to C1 as the wheel and C2 as 1 Several the frame, even when the shapes Spirograph- aren’t circular. -
Additive Manufacturing Application for a Turbopump Rotor
EDITORIAL Identificarea nevoii societale (1) Fie că este vorba de ştiinţă sau de politică, Max Weber viza acelaşi scop: să extragă etica specifică unei activităţi pe care o dorea conformă cu finalitatea sa Raymond ARON Viața oricărei persoane moderne este asociată, mai mult sau mai puțin conștient, așteptării societale. Putem spune că suntem imersați în așteptare, că depindem de ea și o influențăm. Cumpărăm mărfuri din magazine mici ori hipermarketuri, ne instruim în școli și universități, folosim produse realizate în fabrici, avem relații cu băncile. Ca o concluzie, suntem angajați ai unor instituții/organizații și clienți ai altora. Toate aceste lucruri determină o creștere mai mare ca niciodată a valorii organizațiilor și a activităților organizaționale. Teoria organizației este o știință bine formată, fondator al acestei discipline fiind considerat sociologul, avocatul, economistul și istoricului german Max Weber (1864-1920) cel care a trasat așa-numita direcție birocratică în dezvoltarea teoriei managementului și organizării. În scrierile sale despre raționalizarea societății, căutând un răspuns la întrebarea ce trebuie făcut pentru ca întreaga organizație să funcționeze ca o mașină, acesta a subliniat că ordinea, susținută de reguli relevante, este cea mai eficientă metodă de lucru pentru orice grup organizat de oameni. El a considerat că organizația poate fi descompusă în părțile componente și se poate normaliza activitatea fiecăreia dintre aceste părți, a propus astfel să se reglementeze cu precizie numărul și funcțiile angajaților și ale organizațiilor, a subliniat că organizația trebuie administrată pe o bază rațională/impersonală. În acest punct, aspectul social al organizației este foarte important, oamenii fiind recunoscuți pentru ideile, caracterul, relațiile, cultura și deloc de neglijat, așteptările lor. -
On the Topology of Hypocycloids
ON THE TOPOLOGY OF HYPOCYCLOIDS ENRIQUE ARTAL BARTOLO AND JOSE´ IGNACIO COGOLLUDO-AGUST´IN Abstract. Algebraic geometry has many connections with physics: string theory, enumerative geometry, and mirror symmetry, among others. In par- ticular, within the topological study of algebraic varieties physicists focus on aspects involving symmetry and non-commutativity. In this paper, we study a family of classical algebraic curves, the hypocycloids, which have links to physics via the bifurcation theory. The topology of some of these curves plays an important role in string theory [3] and also appears in Zariski’s foundational work [9]. We compute the fundamental groups of some of these curves and show that they are in fact Artin groups. 1. Introduction Hypocycloid curves have been studied since the Renaissance (apparently D¨urer in 1525 described epitrochoids in general and then Roemer in 1674 and Bernoulli in 1691 focused on some particular hypocycloids, like the astroid, see [5]). Hypocy- cloids are described as the roulette traced by a point P attached to a circumference S of radius r rolling about the inside of a fixed circle C of radius R, such that r 1 0 < ρ = R < 2 (see Figure 1). If the ratio ρ is rational, an algebraic curve is ob- tained. The simplest (non-trivial) hypocycloid is called the deltoid or the Steiner curve and has a history of its own both as a real and complex curve. S r C P arXiv:1703.08308v1 [math.AG] 24 Mar 2017 R Figure 1. Hypocycloid Key words and phrases. hypocycloid curve, cuspidal points, fundamental group. -
Hypocycloid Motion in the Melvin Magnetic Universe
Hypocycloid motion in the Melvin magnetic universe Yen-Kheng Lim∗ Department of Mathematics, Xiamen University Malaysia, 43900 Sepang, Malaysia May 19, 2020 Abstract The trajectory of a charged test particle in the Melvin magnetic universe is shown to take the form of hypocycloids in two different regimes, the first of which is the class of perturbed circular orbits, and the second of which is in the weak-field approximation. In the latter case we find a simple relation between the charge of the particle and the number of cusps. These two regimes are within a continuously connected family of deformed hypocycloid-like orbits parametrised by the magnetic flux strength of the Melvin spacetime. 1 Introduction The Melvin universe describes a bundle of parallel magnetic field lines held together under its own gravity in equilibrium [1, 2]. The possibility of such a configuration was initially considered by Wheeler [3], and a related solution was obtained by Bonnor [4], though in today’s parlance it is typically referred to as the Melvin spacetime [5]. By the duality of electromagnetic fields, a similar solution consisting of parallel electric fields can be arXiv:2004.08027v2 [gr-qc] 18 May 2020 obtained. In this paper, we shall mainly be interested in the magnetic version of this solution. The Melvin spacetime has been a solution of interest in various contexts of theoretical high-energy physics. For instance, the Melvin spacetime provides a background of a strong magnetic field to induce the quantum pair creation of black holes [6, 7]. Havrdov´aand Krtouˇsshowed that the Melvin universe can be constructed by taking the two charged, accelerating black holes and pushing them infinitely far apart [8].