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MATHIEU EQUATION AND ITS APPLICATION – MATHEMATICS AND STATISTICS Project Topics – Complete project material

[ad_1] 1.1BriefReviewonMathieuequation Mathieu equation isa specialcase of a linear second order homogeneousdifferentialequation(Ruby1995).Theequationwasfirstdiscussedin1868,byEmileLeonardMathieuinconnectionwithproblemofvibrationsinellipticalmembrane.HedevelopedtheleadingtermsoftheseriessolutionknownasMathieufunctionoftheellipticalmembranes.Adecadelater,HeinedefinedtheperiodicMathieuAngularFunctionsofintegerorderasFouriercosineandsineseries;furthermore,withoutevaluatingthecorrespondingcoefficient,Heobtainedatranscendentalequationforcharacteristicnumbersexpressedintermsofinfinitecontinuedfractions;andalsoshowedthatonesetofperiodicfunctionsofintegerordercouldbeinaseriesofBesselfunction(Chaos-CadorandLey-Koo2002).Intheearly1880’s,FloquetwentfurthertopublishatheoryandthusasolutiontotheMathieudifferentialequation;hisworkwasnamedafterhimas,‘Floquet’sTheorem’or‘Floquet’sSolution’.StephensonusedanapproximateMathieuequation,andproved,thatitispossibletostabilizetheupperpositionofarigidpendulumbyvibratingitspivotpointverticallyataspecifichighfrequency.(StépánandInsperger2003).Thereexistsanextensiveliteratureontheseequations;andinparticular,awell-highexhaustivecompendiumwasgivenbyMc-Lachlan(1947).TheMathieufunctionwasfurtherinvestigatedbynumberofresearcherswhofoundaconsiderableamountofmathematicalresultsthatwerecollectedmorethan60yearsagobyMc-Lachlan(Gutiérrez-Vegaaetal2002).Whittakerandotherscientistderivedin1900sderivedthehigher-ordertermsoftheMathieudifferentialequation.AvarietyoftheequationexistintextbookwrittenbyAbramowitzandStegun(1964).Mathieudifferentialequationoccursintwomaincategoriesofphysicalproblems.First,applicationsinvolvingellipticalgeometriessuchas,analysisofvibratingmodes2inellipticmembrane,thepropagatingmodesofellipticpipesandtheoscillationsofwaterinalakeofellipticshape.Mathieuequationarisesafterseparatingthewaveequation using ellipticcoordinates.Secondly,problemsinvolving periodicmotionexamplesare,thetrajectoryofan electron in aperiodicarrayofatoms,themechanicsofthequantumpendulumandtheoscillationoffloatingvessels.ThecanonicalformfortheMathieudifferentialequationisgivenby+ y =0, (1.1)dy 2dx2 [a-2qcos(2x)](x)whereaandqarerealconstantsknownasthecharacteristicvalueandparameterrespectively.Closely related to the Mathieu differentialequation is the Modified Mathieudifferentialequationgivenby:- y =0, (1.2)dy…

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STATISTICAL ANALYSIS OF FEDERAL GOVERNMENT'S EXPENDITURE AND REVENUE FROM 2003-2008 ( A CASE STUDY NBS, KADUNA) – MATHEMATICS AND STATISTICS Project Topics – Complete project material

[ad_1] TABLE OF CONTENTS Title page Declaration Certification Dedication Acknowledgement Table of Contents Abstracts CHAPTER ONE: INTRODUCTION 1.0     Introduction 1.1     Historical Background of the Study 1.2     Aims of the Study 1.3     Objectives of the Study…

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A TIME SERIES ANALYSIS OF THE MONTHLY DISTRIBUTION OF RAINFALL IN ENUGU METROPOLIS – MATHEMATICS AND STATISTICS Project Topics – Complete project material

[ad_1] ABSTRACT It is widely accepted that water supply will be a pressing issue in this century. Thus, position of adequate rainfall in the development of human and natural resources is a worthwhile research work.…

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A STATISTICAL UNIVARIATE ANALYSIS OF THE GENERAL RESPONSE OF LOCAL DOGS – MATHEMATICS AND STATISTICS Project Topics – Complete project material

[ad_1] CHAPTER ONE 1.1. INTRODUCTION Vaccination of dogs generally is of utmost importance to us seeing that dog is man’s best friend. Vaccinating dogs not only helps to save dogs from infections but it also…

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A STATISTICAL UNIVARIATE ANALYSIS OF THE GENERAL RESPONSE OF LOCAL DOGS TO VACCINATION – MATHEMATICS AND STATISTICS Project Topics – Complete project material

[ad_1] CHAPTER ONE 1.1. INTRODUCTION Vaccination of dogs generally is of utmost importance to us seeing that dog is man’s best friend. Vaccinating dogs not only helps to save dogs from infections but it also…

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MATRIX AND ITS APPLICATIONS – MATHEMATICS AND STATISTICS Project Topics – Complete project material

[ad_1] The introduction and development of the notion of a matrix and the subject of linear algebra followed the development of determinants, which arose from the study of coefficients of systems of linear equations. Leibnitz,…

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DIFFERENTIATION AND ITS APPLICATION – MATHEMATICS AND STATISTICS Project Topics – Complete project material

[ad_1] CHAPTER ONE 1.1  INTRODUCTION From the beginning of time man has been interested in the rate at which physical and non physical things change. Astronomers, physicists, chemists, engineers, business enterprises and industries strive to…

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STATISTICAL ANALYSIS OF CRIMINAL OFFENCES RECORDED IN KUJE – ABUJA (FCT) FROM 1999 – 2007 – MATHEMATICS AND STATISTICS Project Topics – Complete project material

[ad_1] CHAPTER ONE 1.1     INTRODUCTION The increasing desire of the government and civilization to improve the maintenance of law and order and to engage in crime prevention, has led to the search for data on…

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STATISTICAL ANALYSIS OF THE FEDERAL GOVERNMENT’S EXPENDITURE AND REVENUE – MATHEMATICS AND STATISTICS Project Topics – Complete project material

[ad_1] CHAPTER ONE 1.0     INTRODUCTION Public finance is a field of economics concerned with how government raises money, how that money is spent and the effect of these activities on the economy and on the…

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TIME SERIES ANALYSIS ON PATIENT ATTENDANCE – MATHEMATICS AND STATISTICS Project Topics – Complete project material

[ad_1] CHAPTER ONE 1.1    INTRODUCTION Hajia Gambo Sawaba General Hospital since its inception in 1975 has received considerable amount of people, for treatment medical advice, family planning and a host of other reason. Different categories…

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