...real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots. Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers. Logarithms and their properties. Permutations and combinations, Binomial theorem for a positive integral index, properties of binomial coefficients. Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, determinant of a square matrix of order up to three, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables. Addition and multiplication rules of probability, conditional probability, Bayes Theorem, independence of events, computation of probability of events using permutations and combinations. Trigonometry: Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations. Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle, inverse trigonometric...
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...simulation techniques for nanoscale optics and photonics a I. Tsukerman*a, F. Čajkoa, A.P. Sokolovb Department of Electrical & Computer Engineering, The University of Akron, OH 44325-3904, USA b Department of Polymer Science, The University of Akron, OH 44325-3909, USA ABSTRACT Several classes of computational methods are available for computer simulation of electromagnetic wave propagation and scattering at optical frequencies: Discrete Dipole Approximation, the T-matrix − Extended Boundary Condition methods, the Multiple Multipole Method, Finite Difference (FD) and Finite Element (FE) methods in the time and frequency domain, and others. The paper briefly reviews the relative advantages and disadvantages of these simulation tools and contributes to the development of FD methods. One powerful tool – FE analysis − is applied to optimization of plasmon-enhanced AFM tips in apertureless near-field optical microscopy. Another tool is a new FD calculus of “Flexible Local Approximation MEthods” (FLAME). In this calculus, any desirable local approximations (e.g. scalar and vector spherical harmonics, Bessel functions, plane waves, etc.) are seamlessly incorporated into FD schemes. The notorious ‘staircase’ effect for slanted and curved boundaries on a Cartesian grid is in many cases eliminated – not because the boundary is approximated geometrically on a fine grid but because the solution is approximated algebraically by suitable basis functions. Illustrative examples include problems...
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...1. Module Name: Introductory Econometrics Code: P12205 Credits: 10 Semester: Spring 2011/12 Delivery: 16 one-hour lectures + 4 one-hour workshops Aims: The main aims of this module are: to introduce students to the principles, uses and interpretation of regression analysis most commonly employed in applied economics; to provide participants with sufficient knowledge of regression methods to critically evaluate and interpret empirical research. On completion of this module students should be able to: demonstrate understanding of the assumptions and properties underlying regression analysis and the principle of ‘least squares’; interpret and manipulate the coefficients of multiple regression and performance criteria; conduct diagnostic checking of the validity of regression equations coefficients; appreciate the problems of misspecification, multicollinearity, heteroscedasticity and autocorrelation. Content: 1. Simple Regression Analysis 2. Multiple Regression Analysis 3. Dummy Variables 4. Heteroscedasticity 5. Autocorrelation Main Textbook: Dougherty, C. (2011). Introduction to Econometrics, 4th edition, Oxford. 2. Module Name: Computational Finance Code: P12614 Credits: 10 Semester: Spring 2011/12 Programme classes: 12 1-2 hour lectures/workshops Aims: The module aims to describe and analyse the general finance topics and introduces students to implement basic computational approaches to financial problems using Microsoft Excel. It stresses...
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...INTRODUCTION TO THE ESSENTIALS OF TENSOR CALCULUS ******************************************************************************** I. Basic Principles ...................................................................... 1 II. Three Dimensional Spaces ............................................................. 4 III. Physical Vectors ...................................................................... 8 IV. Examples: Cylindrical and Spherical Coordinates .................................. 9 V. Application: Special Relativity, including Electromagnetism ......................... 10 VI. Covariant Differentiation ............................................................. 17 VII. Geodesics and Lagrangians ............................................................. 21 ******************************************************************************** I. Basic Principles We shall treat only the basic ideas, which will suffice for much of physics. The objective is to analyze problems in any coordinate system, the variables of which are expressed as qj(xi) or q'j(qi) where xi : Cartesian coordinates, i = 1,2,3, ....N for any dimension N. Often N=3, but in special relativity, N=4, and the results apply in any dimension. Any well-defined set of qj will do. Some explicit requirements will be specified later. An invariant is the same in any system of coordinates. A vector, however, has components which depend upon the system chosen. To determine how the components change (transform)...
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...ECON1202 Quantitative Analysis for Business and Economics Course Outline Semester 1, 2014 Part A: Course-Specific Information Students are also expected to have read and be familiar with Part B Supplement to All Course Outlines. This contains Policies on Student Responsibilities and Support, Including Special Consideration, Plagiarism and Key Dates. It also contains the ASB PROGRAM LEARNING GOALS. Table of Contents 1 STAFF CONTACT DETAILS 1 1 1 2 2 2 2 2 3 3 5 5 5 5 6 7 7 8 8 8 8 9 10 11 11 11 12 13 13 15 1.1 Communications with staff 1.2 Pitstop and PASS 2 COURSE DETAILS 2.1 Teaching Times and Locations 2.2 Units of Credit 2.3 Summary of Course 2.4 Aims and Relationship to Other Courses 2.5 Presumed Knowledge 2.6 Student Learning Outcomes 3 LEARNING AND TEACHING ACTIVITIES 3.1 Approach to Learning and Teaching in the Course 3.2 Learning Activities and Teaching Strategies 3.2.1 Lectures 3.2.2 3.2.3 3.2.4 4 Tutorials Computing component Out-of-Class Study ASSESSMENT 4.1 Formal Requirements 4.2 Assessment Details 4.3 Tutorial Participation 4.4 Online Quizzes 4.5 In-tutorial Tests 4.6 Final Exam Format 4.7 Quality Assurance 5 6 7 COURSE EVALUATION AND DEVELOPMENT COURSE RESOURCES COURSE SCHEDULE 7.1 Lecture Schedule 7.2 Tutorial Schedule 1 STAFF CONTACT DETAILS Lecturer-in-charge: Dr Arpita Chatterjee Room: ASB 430C Phone: No: 9385 4314 Email: arpita.chatterjee@unsw.edu.au Consultation Times: Tuesday 2 – 5 pm Lecturer: Dr April Cai Room 432, ASB Building Ph 9385...
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...systems. Fourier series representation of continuous periodic signals; sampling theorem; Fourier, Laplace and Z transforms. Electrical Machines: Single phase transformer - equivalent circuit, phasor diagram, tests, regulation and efficiency; three phase transformers - connections, parallel operation; auto-transformer; energy conversion principles. DC machines - types, windings, generator characteristics, armature reaction and commutation, starting and speed control of motors; three phase induction motors - principles, types, performance characteristics, starting and speed control; single phase induction motors; synchronous machines - performance, regulation and parallel operation of generators, motor starting, characteristics and applications; servo and stepper motors. Power Systems: Basic power generation concepts; transmission line models and performance; cable performance, insulation; corona and radio interference; distribution systems; per-unit quantities; bus impedance and admittance matrices; load flow; voltage control. Power factor correction; economic operation; symmetrical components; fault analysis; principles of over-current, differential and distance protection; solid state relays and digital...
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...its Application | Chapter-01: Introduction | 1-3 | 1.1 Background of the Study | 1 | 1.2 Origin of the Study | 2 | 1.3 Objective of the Study | 2 | 1.4 Methodology of the Study | 3 | 1.5 Scope and Limitation of the Study | 3 | Chapter-02: Theoretical Overview | 4-8 | 2.1 Definition of Matrix | 4 | 2.2 Matrix Notation | 4 | 2.3 History of Matrix | 5 | 2.4 Types of Matrix | 6 | 2.4.1 Row Matrix | 6 | 2.4.2 Column Matrix | 6 | 2.4.3 Rectangular Matrix | 6 | 2.4.4 Square Matrix | 6 | 2.4.5 Zero Matrix | 7 | 2.4.6 Upper Triangular Matrix | 7 | 2.4.7 Lower Triangular Matrix | 7 | 2.4.8 Diagonal Matrix | 7 | 2.4.9 Scalar Matrix | 7 | 2.4.10 Identity Matrix | 8 | 2.4.11 Transpose Matrix | 8 | 2.4.12 Regular Matrix | 8 | 2.4.13 Singular Matrix | 8 | Chapter-03: Matrices Operation | 9-15 | 3.1. Properties of matrix operation | 9 | 3.1.1 Properties of subtraction | 9 | 3. 1.2 Properties of Addition | 9 | 3.1.3 Properties of Matrix Multiplication | 10 | 3.1.4 Properties of Scalar Multiplication | 10 | 3.1.5 Properties of the Transpose of a Matrix | 10 | 3.2 Matrix Operation | 11 | 3.2.1 Matrix Equality | 12 | 3.2.2 Matrix Addition | 12 | 3.2.3 Matrix Subtraction | 12 | 3.2.4 Matrix Multiplication | 12 | 3.2.5 Multiplication of Vectors | 14 | 3.3 Inverse of Matrix | 15 | 3.4 Elementary Operations | 15 | Chapter-04: Application of Matrix | 16-21 | 4.1 Application of Matrix | 16...
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... Calculus From Wikipedia, the free encyclopedia Jump to: navigation, search This article is about the branch of mathematics. For other uses, see Calculus (disambiguation). | It has been suggested that Infinitesimal calculus be merged into this article or section. (Discuss) Proposed since May 2011. | Topics in Calculus | Fundamental theorem Limits of functions Continuity Mean value theorem [show]Differential calculus | Derivative Change of variables Implicit differentiation Taylor's theorem Related rates Rules and identities:Power rule, Product rule, Quotient rule, Chain rule | [show]Integral calculus | IntegralLists of integrals Improper integrals Integration by: parts, disks, cylindrical shells, substitution, trigonometric substitution, partial fractions, changing order | [show]Vector calculus | Gradient Divergence Curl Laplacian Gradient theorem Green's theorem Stokes' theorem Divergence theorem | [show]Multivariable calculus | Matrix calculus Partial derivative Multiple integral Line integral Surface integral Volume integral Jacobian | | Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the...
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...Ch. 4 Case Study Job Requirement Matrix for Sale Associate |Job Duty |Tasks |Relative |Relative Time |Competency or KSAO |Importance of KSAO or | | | |Importance of Job|Spent (%) | |Competency to Task | | | |Duty (%) | | |Performance (1 = low, | | | | | | |10 = high),( E = | | | | | | |essential) | | Customer Service |1. Greet customers and ascertain what |35 |50 |1. Knowledge of principles and |10 E | | |each customer wants or needs. | | |processes for providing customer | | | |2. Answer questions regarding the store | | |and personal services. | | | |and its merchandise. | | |2. Active listening skills...
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...1 SPRING, 2014-2015 SCIENCE AND INFORMATION TECHNOLOGY Class Id 00001 00002 00003 00004 00005 00006 Course Name ADVANCED COMPUTER NETWORKS LABORATORY ADVANCED COMPUTER NETWORKS LABORATORY ADVANCED COMPUTER NETWORKS LABORATORY ADVANCED COMPUTER NETWORKS LABORATORY ADVANCED TOPICS IN PROGRAMMING III LABORATORY ALGORITHM LABORATORY 00007 00008 00009 00010 00011 00012 00013 00014 00015 00016 00017 00018 ALGORITHM LABORATORY ALGORITHM LABORATORY ALGORITHM LABORATORY ALGORITHM LABORATORY ALGORITHM LABORATORY ALGORITHM LABORATORY ARTIFICIAL INTELLIGENCE AND EXPERT SYSTEM LABORATORY ARTIFICIAL INTELLIGENCE AND EXPERT SYSTEM LABORATORY ARTIFICIAL INTELLIGENCE AND EXPERT SYSTEM LABORATORY ARTIFICIAL INTELLIGENCE AND EXPERT SYSTEM LABORATORY COMPUTER GRAPHICS LABORATORY COMPUTER GRAPHICS LABORATORY 00019 00020 00021 COMPUTER GRAPHICS LABORATORY COMPUTER GRAPHICS LABORATORY COMPILER DESIGN A D C B A D C B A G F E D C B A A B C D Sec A Time 12:0-2:0 11:0-2:0 10:0-12:0 11:0-2:0 4:0-6:0 2:0-5:0 4:0-6:0 5:0-8:0 4:0-6:0 5:0-8:0 08:0-10:0 08:0-11:0 10:0-12:0 08:0-11:0 12:0-2:0 11:0-2:0 2:0-4:0 2:0-5:0 08:0-10:0 08:0-11:0 4:0-6:0 08:0-11:0 4:0-6:0 5:0-8:0 2:0-4:0 2:0-5:0 4:0-6:0 11:0-2:0 12:0-2:0 11:0-2:0 4:0-6:0 5:0-8:0 08:0-10:0 08:0-11:0 10:0-12:0 08:0-11:0 12:0-2:0 11:0-2:0 2:0-4:0 2:0-5:0 12:30-2:0 Day T S W M S T T S M W S T M W T S W M M W W TH S T T S T TH W M M W W M T S W M T S ST RM 441 CL8 441 CL8 441 CL8 422 CL7 424 CL5 441 CL3 441 CL2 431 CL3 431 CL3 434 CL6 434 CL6 424 CL3 441 CL4...
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...(coereq: 6F:100) 6F:103 Property and Liability Insurance (prereq: 6F:102); or 6F:104 Corp Fin Risk Mgt (prereq: 6F:102, coreq 6F:110); or 6F:105 Life and Health Insurance (prereq: 6F:102); or 6F:106 Employee Benefit Plans (prereq: 6F:102) 6F:108 Topics in Finance I (SP 09 or later, prereq: 6F:100) 6F:109 Topics in Finance II (prereq: 6F:100) 6F:112 Applied Equity Valuation (prereq: 6F:100) (req: 2.80 UI GPA). See Finance Department for special permission. sh grade 2 3 3 3 3 3 *If you entered UI prior to Summer 2011, check your degree audit for specific req’s. **The fourth-level proficiency in a single foreign language or the second-level proficiency in two different foreign languages. II. Prerequisites (22 sh) 22M:017 Calculus and Matrix Algebra for Business (req: 22M:13 or satisfactory score on placement exam) 3 3 3 sh grade 4 22S:008 Statistics...
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...University of Phoenix Material Reliability and Validity Matrix For each of the tests of reliability and validity listed on the matrix, prepare a 50- to 100-word description of the test’s application. Describe what conditions these reliability types would be used for as well as when they would be inappropriate. Then, for each test, prepare a 50- to 100-word description of the strengths and a 50- to 100-word description of the weaknesses. Test of reliability | Application and appropriateness | Advantages | Disadvantages | Internal consistency | Internal consistency is used to make sure that multiple constructs that are measuring a variable produce identical results. An example of the test would be a questionnaire where the respondent is asked questions about cigarettes and he responds that he does not like cigarettes, has not smoked in the past, and disagrees with the statement “I like smoking cigarettes”. This would show a good internal consistency of the questionnaire. | The advantages of internal consistency reliability are that it makes sure that a test is not redundant and that each part of the test is helping to measure the target variable. | The disadvantages of internal consistency reliability are that it does help in understanding if the target variable is being measured by all the questions, but doesn’t say whether it is being measured accurately. | Split-half | The split half reliability test is a test comprising of two sections. Each section’s...
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...Bachelor of Engineering Civil Engineering First Year (First & Second Semester) • ENG Mathematics – I & ENG Mathematics II: 2D & 3D Coordinate Geometry; Differential Calculus; Infinite Series; Matrices,Ordinary differential equations of first and second order; Laplace Transforms; Vector Calculus • Elements of Mechanical Engineering & Elements of Civil Engineering Principle of virtual work,Rectilinear & curvilinear translation; Rotation of a rigid body about a fixed axis; Plane motion of a rigid body,Classification of force systems; Principle of physical independence of forces, Principle of superposition of forces, Principle of transmissibility of forces; Equivalent force – couple system; Resolution of forces, composition of forces; Types of supports, statically determinate beams, Numerical problems on support reactions for statically determinate beams and analysis of simple trusses ,Friction. • Engineering Physics Interference, diffraction and polarization of light; Nuclear fission, fusion, particle accelerators; Wave Particle Duality • Engineering Chemistry Physical Chemistry: Atoms, molecules and solids; phase equilibria; Galvanic & Fuel cells • Organic Chemistry: Types of reactions and reaction mechanisms; Concept of armaticity Computer Concepts & C Programming Introduction to digital computers; problem solving using computers; Programming in Fortran 77: Constants, variables,expressions...
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...THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems ∏ Cătălin Bărboianu INFAROM Publishing Applied Mathematics office@infarom.com http://www.infarom.com http://probability.infarom.ro ISBN 978-973-1991-11-5 Publisher: INFAROM Author: Cătălin Bărboianu Correction Editor: CarolAnn Johnson Copyright © INFAROM 2009 This work is subject to copyright. All rights are reserved, whether the whole work or part of the material is concerned, specifically the rights of translation, reprinting, reuse of formulas and tables, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of Copyright Laws, and permission for use must always be obtained from INFAROM. 2 Contents (of the complete edition) Introduction ...................................................................................... 5 The Rules of Lottery ...................................................................…. 11 Supporting Mathematics ......................................................…....... 15 Probability space ..............................................................…......... 16 Probability properties and formulas used .........................…......... 19 Combinatorics …………………………………………………... 22 Parameters of the lottery matrices …………………………......... 25 Number Combinations .......………….………………………...
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...Mathematics HL First examinations 2008 b DIPLOMA PROGRAMME MATHEMATICS HL First examinations 2008 International Baccalaureate Organization Buenos Aires Cardiff Geneva New York Singapore Diploma Programme Mathematics HL First published in September 2006 International Baccalaureate Organization Peterson House, Malthouse Avenue, Cardiff Gate Cardiff, Wales GB CF23 8GL United Kingdom Phone: + 44 29 2054 7777 Fax: + 44 29 2054 7778 Web site: www.ibo.org c International Baccalaureate Organization 2006 The International Baccalaureate Organization (IBO) was established in 1968 and is a non-profit, international educational foundation registered in Switzerland. The IBO is grateful for permission to reproduce and/or translate any copyright material used in this publication. Acknowledgments are included, where appropriate, and, if notified, the IBO will be pleased to rectify any errors or omissions at the earliest opportunity. IBO merchandise and publications in its official and working languages can be purchased through the IB store at http://store.ibo.org. General ordering queries should be directed to the sales and marketing department in Cardiff. Phone: +44 29 2054 7746 Fax: +44 29 2054 7779 E-mail: sales@ibo.org Printed in the United Kingdom by Antony Rowe Ltd, Chippenham, Wiltshire. 5007 CONTENTS INTRODUCTION 1 NATURE OF THE SUBJECT 3 AIMS 6 OBJECTIVES 7 SYLLABUS OUTLINE 8 SYLLABUS DETAILS 9 ASSESSMENT OUTLINE 53 ASSESSMENT DETAILS ...
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