LEADER 02733nas 2200493-a 450 001 996216089903316 005 20200604065528.4 035 $a(OCoLC)70254280 035 $a(CKB)1000000000312868 035 $a(CONSER)--2006214870 035 $a(DE-599)ZDB2434924-0 035 $a(EXLCZ)991000000000312868 100 $a20060706a20079999 s-- a 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aJournal of Mesoamerican languages and linguistics 210 $aChapel Hill, NC $cUniversity of North Carolina at Chapel Hill, Dept. of Linguistics 311 $a1932-4413 330 $aThe goal of the Journal of Mesoamerican Languages and Linguistics (JMLL) is to contribute to the documentation of Mesoamerican languages, many of which are endangered, as well as to their historical, theoretical, and typological analysis. Some topics that the Editorial Board of this journal hopes to develop further, due to the dearth of relevant publications in the past, include the following: Mesoamerican sociolinguistics (with its potential for elucidating aspects related to language socialization and language endangerment), the history of Mesoamerican linguistics, and the study of indigenous sign languages (or related systems). Other topics that are encouraged include: the linguistic structure of indigenous writing systems and texts (from any time period), and possible historical relationships (whether by common descent or contact) between Mesoamerican languages and non-Mesoamerican languages-- not to mention further research on the nature of Mesoamerica as a linguistic area. 517 1 $aMesoamerican languages and linguistics 517 1 $aJMLL 531 $aJOURNAL OF MESOAMERICAN LANGUAGES & LINGUISTICS 531 0 $aJournal of Mesoamerican languages and linguistics 606 $aMayan languages$xSocial aspects$vPeriodicals 606 $aMayan languages$xSocial aspects$2fast$3(OCoLC)fst01012766 606 $aSociolinguistics$2fast$3(OCoLC)fst01123847 607 $aCentral America$xLanguages$xSocial aspects$vPeriodicals 607 $aMexico$xLanguages$xSocial aspects$vPeriodicals 607 $aCentral America$2fast 607 $aMexico$2fast 608 $aPeriodicals.$2fast 608 $aPeriodicals.$2lcgft 615 0$aMayan languages$xSocial aspects 615 7$aMayan languages$xSocial aspects. 615 7$aSociolinguistics. 676 $a497.4 712 02$aUniversity of North Carolina at Chapel Hill.$bDepartment of Linguistics, 906 $aJOURNAL 912 $a996216089903316 996 $aJournal of Mesoamerican languages and linguistics$92167116 997 $aUNISA LEADER 11448nam 22005053 450 001 9910838333803321 005 20230310080256.0 010 $a9781683928737$b(electronic bk.) 010 $z9781683928744 035 $a(MiAaPQ)EBC30405189 035 $a(Au-PeEL)EBL30405189 035 $a(CKB)26240869600041 035 $a(BIP)089053967 035 $a(EXLCZ)9926240869600041 100 $a20230310d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematical Modeling 205 $a1st ed. 210 1$aBloomfield :$cMercury Learning & Information,$d2023. 210 4$dİ2023. 215 $a1 online resource (287 pages) 311 08$aPrint version: Kapur, J. N. Mathematical Modeling Bloomfield : Mercury Learning & Information,c2023 9781683928744 327 $aCover -- Title Page -- Copyright -- Contents -- Preface -- Chapter 1: Mathematical Modeling: Need, Techniques, Classifications, and Simple Illustrations -- 1.1 Simple Situations Requiring Mathematical Modeling -- 1.2 The Technique of Mathematical Modeling -- 1.3 Classification of Mathematical Models -- 1.4 Some Characteristics of Mathematical Models -- 1.5 Mathematical Modeling through Geometry -- 1.6 Mathematical Modeling through Algebra -- 1.7 Mathematical Modeling through Trigonometry -- 1.7.1 Finding the Distance of the Moon -- 1.7.2 Finding the Distance of a Star -- 1.7.3 Finding Length of the Day -- 1.8 Mathematical Modeling through Calculus -- 1.8.1 Law of Reflection -- 1.8.2 Law of Refraction of Light -- 1.8.3 EOQ Model for Inventory Control -- 1.8.4 Triangle of Given Perimeter with Maximum Area -- 1.8.5 Parallelopiped with Given Perimeter and Maximum Volume -- 1.8.6 Mathematics of Business -- 1.9 Limitations of Mathematical Modeling -- Bibliography -- Chapter 2: Mathematical Modeling through Ordinary Differential Equations of the First Order -- 2.1 Mathematical Modeling through Differential Equations -- 2.2 Linear Growth and Decay Models -- 2.2.1 Populational Growth Models -- 2.2.2 Growth of Science and Scientists -- 2.2.3 Effects of Immigration and Emigration on Population Size -- 2.2.4 Interest Compounded Continuously -- 2.2.5 Radioactive Decay -- 2.2.6 Decrease of Temperature -- 2.2.7 Diffusion -- 2.2.8 Change of Price of a Commodity -- 2.3 Nonlinear Growth and Decay Models -- 2.3.1 Logistic Law of Population Growth -- 2.3.2 Spread of Technological Innovations and Infectious Diseases -- 2.3.3 Rate of Dissolution -- 2.3.4 Law of Mass Action: Chemical Reactions -- 2.4 Compartment Models -- 2.4.1 A Simple Compartment Model -- 2.4.2 Diffusion of Glucose or a Medicine in the Bloodstream -- 2.4.3 The Case of a Succession of Compartments. 327 $a2.5 Mathematical Modeling In Dynamics through Ordinary Differential Equations of the First Order -- 2.5.1 Simple Harmonic Motion -- 2.5.2 Motion Under Gravity in a Resisting Medium -- 2.5.3 Motion of a Rocket -- 2.6 Mathematical Modeling of Geometrical Problems through Ordinary Differential Equations of the First Order -- 2.6.1 Simple Geometrical Problems -- 2.6.2 Orthogonal Trajectories -- Chapter 3: Mathematical Modeling through Systems of Ordinary Differential Equations of the First Order -- 3.1 Mathematical Modeling In Population Dynamics -- 3.1.1 Prey-Predator Models -- 3.1.2 Competition Models -- 3.1.3 Multispecies Models -- 3.1.4 Age-Structured Population Models -- 3.2 Mathematical Modeling of Epidemics through Systems of Ordinary Differential Equations of the First Order -- 3.2.1 A Simple Epidemic Model -- 3.2.2 A Susceptible-Infected-Susceptible (SIS) Model -- 3.2.3 SIS Model with Constant Number of Carriers -- 3.2.4 Simple Epidemic Model with Carriers -- 3.2.5 Model with Removal -- 3.2.6 Model with Removal and Immigration -- 3.3 Compartment Models through Systems of Ordinary Differential Equations -- 3.4 Mathematical Modeling In Economics Based On Systems of Ordinary Differential Equations of the First Order -- 3.4.1 Domar Macro Model -- 3.4.2 Domar First Debt Model -- 3.4.3 Domar's Second Debt Model -- 3.4.4 Allen's Speculative Model -- 3.4.5 Samuelson's Investment Model -- 3.4.6 Samuelson's Modified Investment Model -- 3.4.7 Stability of Market Equilibrium -- 3.4.8 Leontief's Open and Closed Dynamical Systems for Inter-Industry Relations -- 3.5 Mathematical Models in Medicine, Arms Race Battles, and International Trade In Terms of Systems of Ordinary Differential Equations -- 3.5.1 A Model for Diabetes Mellitus -- 3.5.2 Richardson's Model for the Arms Race -- 3.5.3 Lanchester's Combat Model -- 3.5.4 International Trade Model. 327 $a3.6 Mathematical Modeling In Dynamics through Systems of Ordinary Differential Equations of the First Order -- 3.6.1 Modeling in Dynamics -- 3.6.2 Motion of a Projectile -- 3.6.3 External Ballistics of Gun Shells -- Chapter 4: Mathematical Modeling through Ordinary Differential Equations of the Second Order -- 4.1 Mathematical Modeling of Planetary Motions -- 4.1.1 Need for the Study of Motion Under Central Forces -- 4.1.2 Components of Velocity and Acceleration Vectors along Radial and Transverse Directions -- 4.1.3 Motion Under a Central Force -- 4.1.4 Motion Under the Inverse Square Law -- 4.1.5 Kepler's Laws of Planetary Motions -- 4.2 Mathematical Modeling of Circular Motion and Motion of Satellites -- 4.2.1 Circular Motion -- 4.2.2 Motion of a Particle on a Smooth or Rough Vertical Wire -- 4.2.3 Circular Motion of Satellites -- 4.2.4 Elliptic Motion of Satellites -- 4.3 Mathematical Modeling through Linear Differential Equations of the Second Order -- 4.3.1 Rectilinear Motion -- 4.3.2 Electrical Circuits -- 4.3.3 Phillip's Stabilization Model for a Closed Economy -- 4.4 Miscellaneous Mathematical Models through Ordinary Differential Equations of the Second Order -- 4.4.1 The Catenary -- 4.4.2 A Curve of Pursuit -- Chapter 5: Mathematical Modeling through Difference Equations -- 5.1 The Need For Mathematical Modeling through Difference Equations: Some Simple Models -- 5.2 Basic Theory of Linear Difference Equations With Constant Coefficients -- 5.2.1 The Linear Difference Equation -- 5.2.2 The Complementary Function -- 5.2.3 The Particular Solution -- 5.2.4 Obtaining the Complementary Function by Use of Matrices -- 5.2.5 Solution of a System of Linear Homogeneous Difference Equations with Constant Coefficients -- 5.2.6 Solution of Linear Difference Equations by Using the Laplace Transform. 327 $a5.2.7 Solution of Linear Difference Equations by Using the z-Transform -- 5.2.8 Solution of Nonlinear Difference Equations Reducible to Linear Equations -- 5.2.9 Stability Theory for Difference Equations -- 5.3 Mathematical Modeling through Difference Equations In Economics And Finance -- 5.3.1 The Harrod Model -- 5.3.2 The Cobweb Model -- 5.3.3 Samuelson's Interaction Models -- 5.3.4 Application to Actuarial Science -- 5.4 Mathematical Modeling through Difference Equations In Population Dynamics and Genetics -- 5.4.1 Nonlinear Difference Equations Model for Population Growth: Nonlinear Difference Equations -- 5.4.2 Age-Structured Population Models -- 5.4.3 Mathematical Modeling through Difference Equations in Genetics -- 5.5 Mathematical Modeling through Difference Equations In Probability Theory -- 5.5.1 Markov Chains -- 5.5.2 Gambler's Ruin Problems -- 5.6 Miscellaneous Examples of Mathematical Modeling through Difference Equations -- Chapter 6: Mathematical Modeling through Partial Differential Equations -- 6.1 Situations Giving Rise To Partial Differential Equation Models -- 6.2 Mass Balance Equations: First Method of Getting PDE Models -- 6.2.1 Equation of Continuity in Fluid Dynamics -- 6.2.2 Equation of Continuity for Heat Flow -- 6.2.3 Equation of Continuity for Traffic Flow on a Highway -- 6.2.4 Gauss Divergence Theorem in Electrostatics -- 6.2.5 Mathematical Modeling in Terms of Laplace's Equation -- 6.2.6 Mathematical Modeling in Terms of the Diffusion Equation -- 6.3 Momentum Balance Equations: the Second Method of Obtaining Partial Differential Equation Models -- 6.3.1 Euler's Equations of Motion for Inviscid Fluid Flow -- 6.3.2 Partial Differential Equation Model for a Vibrating String -- 6.3.3 Partial Differential Equation Model for a Vibrating Membrane -- 6.3.4 Mathematical Modeling in Terms of the Wave Equation. 327 $a6.4 Variational Principles: Third Method of Obtaining Partial Differential Equation Models -- 6.4.1 Euler-Lagrange Equation -- 6.4.2 Minimal Surfaces -- 6.4.3 Vibrating String -- 6.4.4 Vibrating Membrane -- 6.4.5 Gas Filled Cylinder -- 6.5 Probability Generating Function, Fourth Method of Obtaining Partial Differential Equation Models -- 6.5.1 PDE Model for Birth-Death-Immigration-Emigration Process -- 6.5.2 PDE Model for a Stochastic Epidemic Process with No Removal -- 6.5.3 Stochastic Epidemic Model with No Removal -- 6.6 Model For Traffic On A Highway -- 6.6.1 Relation Between Car Velocity U and Traffic Density ? -- 6.6.2 An Alternative Relation Between U and ? -- 6.6.3 Traffic Wave Propagation Along a Highway -- 6.7 Nature of Partial Differential Equations -- 6.7.1 Elliptic, Parabolic, and Hyperbolic Equations -- 6.7.2 Nature of Three Basic Linear Partial Differential Equations -- 6.7.3 The Nature of the Partial Differential Equation for the Potential of the Steady Two-Dimensional Flow of the Inviscid Flow of an Ideal Gas -- 6.8 Initial and Boundary Conditions -- Chapter 7: Mathematical Modeling through Graphs -- 7.1 Situations That Can Be Modeled through Graphs -- 7.1.1 Qualitative Relations in Applied Mathematics -- 7.1.2 The Seven Bridges Problem -- 7.1.3 Some Types of Graphs -- 7.1.4 Nature of Models in Terms of Graphs -- 7.2 Mathematical Models In Terms of Directed Graphs -- 7.2.1 Representing Results of Tournaments -- 7.2.2 One-Way Traffic Problems -- 7.2.3 Genetic Graphs -- 7.2.4 Senior-Subordinate Relationship -- 7.2.5 Food Webs -- 7.2.6 Communication Networks -- 7.2.7 Matrices Associated with a Directed Graph -- 7.2.8 Application of Directed Graphs to Detection of Cliques -- 7.3 Mathematical Models In Terms of Signed Graphs -- 7.3.1 Balance of Signed Graphs -- 7.3.2 Structure Theorem and its Implications. 327 $a7.3.3 Antibalance and Duobalance of a Graph. 330 8 $aThis book can be used in courses on mathematical modeling at the senior undergraduate or graduate level, or used as a reference for in-service scientists and engineers. The book provides an overview of mathematical modeling through a panoramic view of applications of mathematics in science and technology. In each chapter, mathematical models are chosen from the physical, biological, social, economic, management, and engineering sciences. The models deal with differentconcepts, but have a common mathematical structure and bring out the unifying influence of mathematical modeling in different disciplines.FEATURES:Provides a balance between theory and applicationsFeatures models from the physical, biological, social, economic, management, and engineering sciences 610 $aAlgebras, Linear 610 $aMathematical Optimization 610 $aDifference Equations 610 $aMathematics 676 $a511.8 700 $aKapur$b J. N$01730295 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910838333803321 996 $aMathematical Modeling$94141157 997 $aUNINA