Applied mathematical modeling: a multidisciplinary approach
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton
Chapman & Hall/CRC
2019
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xxiv, 443 Seiten Diagramme |
| ISBN: | 036739930X |
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| adam_text | Contents 1 The Impact and Benefits of Mathematical Modeling 1 1.1 Introduction....................................................................... 1 1.2 Mathematical Aspects, Alternatives, Attitudes............ 1 1.3 Mathematical Modeling..................................................... 5 1.4 Teaching Modeling.............................................................. 9 1.5 Benefits of Modeling........................................................... 11 1.6 Educational Benefits........................................................... 12 1.7 Modeling and Group Competition.................................. 17 1.8 Other Benefits of Modeling.............................................. 19 1.9 The Role of Axioms in Modeling..................................... 22 1.10 The Challenge.................................................................... 24 1.11 References.......................................................................... 25 2 Remarks on Mathematical Model Building 27 2.1 Introduction....................................................................... 27 2.2 An Example of Mathematical Modeling......................... 27 2.3 Model Construction and Validation............................... 29 2.4 Model Analysis.................................................................... 36 2.5 Some Pitfalls....................................................................... 37 2.6 Conclusion.......................................................................... 39 2.7
References.......................................................................... 39 3 Understanding the United States AIDS Epidemic: A Modeler’s Odyssey 3.1 Introduction........................................................................ 41 41 vii
vin 3.2 Prelude: The Postwar Polio Epidemic............................ 42 3.3 AIDS: A New Epidemic for America............................... 43 3.4 Why An AIDS Epidemic in America?............................ 46 3.5 A More Detailed Look at the Model............................... 51 3.6 Forays into the Public Policy Arena............................... 54 3.7 Modeling the Mature Epidemic........................................ 55 3.8 AIDS as a Facilitator of Other Epidemics...................... 57 3.9 Comparisons with First World Countries...................... 58 3.10 Conclusion: A Modeler’s Portfolio.................................. 66 3.11 References.......................................................................... 69 4 A Model for the Spread of Sleeping Sickness 71 4.1 Introduction....................................................................... 71 4.2 The Compartmental Model............................................... 73 4.3 Mathematical Results........................................................ 78 4.4 Discussion........................................................................... 85 4.5 Alternative Models 87 4.6 Exercises and Projects ..................................................... 90 4.7 References........................................................................... 92 ........................................................... 5 Mathematical Models in Classical Cryptology 93 5.1 Introduction........................................................................ 93 5.2 Some Terminology of
Cryptology..................................... 94 5.3 Simple Substitution Systems within a General Crypto graphic Framework ........................................................... 95 5.4 The Vigenére Cipher and One-Time Pads...................... 99 5.5 The Basic Hill System and Variations............................ 103 5.6 Exercises and Projects ..................................................... 107 5.7 References........................................................................... 112 6 Mathematical Models in Public-Key Cryptology 6.1 Introduction......................................................................... 115 115
ix 6.2 Cryptosystems Based on Integer Factorization............ 120 6.3 Cryptosystems Based on Discrete Logarithms................ 126 6.4 Digital Signatures.............................................................. 130 6.5 Exercises and Projects ..................................................... 133 6.6 References.......................................................................... 135 7 Nonlinear Transverse Vibrations in an Elastic Medium 137 7.1 Introduction....................................................................... 137 7.2 A String Embedded in an Elastic Medium ................... 138 7.3 An Approximation Technique for Nonlinear Differential Equations.............................................................................. 141 7.4 Base Equation Solution of Ricatti Equation................... 143 7.5 Exercises and Projects ..................................................... 145 7.6 References.......................................................................... 148 8 Simulating Networks with Time-Varying Arrivals 151 8.1 Introduction....................................................................... 151 8.2 The Registration Problem ............................................... 152 8.3 Generating Random Numbers ........................................ 153 8.4 Statistical Tools................................................................. 160 8.5 Arrival Processes................................................................. 166 8.6 Queueing Models 172 8.7 Exercises and Projects
..................................................... 178 8.8 References.......................................................................... 182 .............................................................. 9 Mathematical Modeling of Unsaturated Porous Media Flow and Transport 185 9.1 Introduction................................................................. ... . 185 9.2 Governing Equations ........................................................ 186 9.3 Constant-Coefficient Convection-Dispersion................... 190 9.4 Coupling the Equations..................................................... 193 9.5 Summary and Suggestions for Further Study................ 198 9.6 Exercises and Projects 200 .....................................................
x 9.7 References......................................................................... 10 Inventory Replenishment Policies and Production Strategies 201 203 10.1 Introduction....................................................................... 203 10.2 Piston Production and the Multinomial Model............ 204 10.3 Sleeve Inventory Safety Stocks........................................ 205 10.4 Comparison of Three Reordering Policies...................... 206 10.5 Variable Piston Production Quantities............................ 210 10.6 The Supplier’s Production Problem............................... 211 10.7 Target Selection for Multinomial Distributions............ 220 10.8 The Supplier’s Cost Function............................................ 222 10.9 Target Selection Using Normal Distributions................ 223 10.10 Conclusion........................................................................... 226 10.11 Exercises and Projects ..................................................... 227 10.12 References........................................................................... 229 11 Modeling Nonlinear Phenomena by Dynamical Systems 231 11.1 Introduction....................................................................... 231 11.2 Simple Pendulum.............................................................. 232 11.3 Periodically Forced Pendulum......................................... 235 11.4 Exercises and Projects ..................................................... 238 11.5
References........................................................................... 240 12 Modulated Poisson Process Models for Bursty Traffic Behavior 241 12.1 Introduction....................................................................... 241 12.2 Workstation Utilization Problem..................................... 242 12.3 Constructing a Modulated Poisson Process................... 244 12.4 Simulation Techniques........................................................ 255 12.5 Analysis Techniques........................................................... 260 12.6 Exercises and Projects ..................................................... 264 12.7 References........................................................................... 268
xi 13 Graph-Theoretic Analysis of FiniteMarkov Chains 271 13.1 Introduction....................................................................... 271 13.2 State Classification ........................................................... 272 13.3 Periodicity.......................................................................... 278 13.4 Conclusion.......................................................................... 286 13.5 Exercises and Projects ..................................................... 286 13.6 References.......................................................................... 289 14 Some Error-Correcting Codes andTheirApplications 291 14.1 Introduction....................................................................... 291 14.2 Background Coding Theory............................................... 292 14.3 Computer Memories and Hamming Codes ................... 301 14.4 Photographs in Space and Reed-Muller Codes............ 305 14.5 Compact Discs and Reed-SolomonCodes....................... 307 14.6 Conclusion.......................................................................... 311 14.7 Exercises and Projects ..................................................... 311 14.8 References.......................................................................... 313 15 Broadcasting and Gossiping in Communication Networks 315 15.1 Introduction....................................................................... 315 15.2 Standard Gossiping and Broadcasting............................ 316 15.3 Examples of
Communication........................................... 321 15.4 Results from Selected Gossiping Problems ................... 327 15.5 Conclusion.......................................................................... 330 15.6 Exercises and Projects ..................................................... 330 15.7 References.......................................................................... 331 16 Modeling the Impact of Environmental Regulations on Hydroelectric Revenues 333 16.1 Introduction....................................................................... 333 16.2 Preliminaries....................................................................... 334 16.3 Model Formulation 336 ...........................................................
Xli 16.4 Model Development........................................................... 342 16.5 Case Study.......................................................................... 350 16.6 Exercises andProjects ...................................................... 359 16.7 References.......................................................................... 362 17 Vertical Stabilization of a Rocket on a Movable Platform 363 17.1 Introduction........................................................................ 363 17.2 Mathematical Model........................................................... 364 17.3 State-Space Control Theory ........................................... 367 17.4 The KNvD Algorithm........................................................ 370 17.5 Exercises and Projects ..................................................... 372 17.6 References........................................................................... 380 18 Distinguished Solutions of a Forced Oscillator 383 18.1 Introduction....................................................................... 383 18.2 Linear Model with ModifiedExternal Forcing................. 385 18.3 Nonlinear Oscillator PeriodicallyForced by Impulses . . 389 18.4 A Suspension Bridge Model............................................... 394 18.5 Model Extension to Two SpatialDimensions................. 398 18.6 Exercises and Projects ..................................................... 399 18.7 References........................................................................... 401 19 Mathematical Modeling and
Computer Simulation of a Polymerization Process 403 19.1 Introduction........................................................................ 403 19.2 Formulating a Mathematical Model............................... 407 19.3 Computational Approach.................................................. 412 19.4 Conclusion........................................................................... 418 19.5 Exercises and Projects ..................................................... 420 19.6 References........................................................................... 422
xiii A The Clemson Graduate Program in the Mathematical Sciences 423 A.l Introduction.......................................................................... 423 A.2 Historical Background........................................................ 424 A.3 Transformation of a Department..................................... 426 A.4 The Clemson Program........................................................ 428 A.5 Communication Skills........................................................ 431 A.6 Program Governance........................................................... 432 A.7 Measures of Success ........................................................... 433 A.8 Conclusion .......................................................................... 435 A.9 References............................................................................. 435 Index 437
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| adam_txt |
Contents 1 The Impact and Benefits of Mathematical Modeling 1 1.1 Introduction. 1 1.2 Mathematical Aspects, Alternatives, Attitudes. 1 1.3 Mathematical Modeling. 5 1.4 Teaching Modeling. 9 1.5 Benefits of Modeling. 11 1.6 Educational Benefits. 12 1.7 Modeling and Group Competition. 17 1.8 Other Benefits of Modeling. 19 1.9 The Role of Axioms in Modeling. 22 1.10 The Challenge. 24 1.11 References. 25 2 Remarks on Mathematical Model Building 27 2.1 Introduction. 27 2.2 An Example of Mathematical Modeling. 27 2.3 Model Construction and Validation. 29 2.4 Model Analysis. 36 2.5 Some Pitfalls. 37 2.6 Conclusion. 39 2.7
References. 39 3 Understanding the United States AIDS Epidemic: A Modeler’s Odyssey 3.1 Introduction. 41 41 vii
vin 3.2 Prelude: The Postwar Polio Epidemic. 42 3.3 AIDS: A New Epidemic for America. 43 3.4 Why An AIDS Epidemic in America?. 46 3.5 A More Detailed Look at the Model. 51 3.6 Forays into the Public Policy Arena. 54 3.7 Modeling the Mature Epidemic. 55 3.8 AIDS as a Facilitator of Other Epidemics. 57 3.9 Comparisons with First World Countries. 58 3.10 Conclusion: A Modeler’s Portfolio. 66 3.11 References. 69 4 A Model for the Spread of Sleeping Sickness 71 4.1 Introduction. 71 4.2 The Compartmental Model. 73 4.3 Mathematical Results. 78 4.4 Discussion. 85 4.5 Alternative Models 87 4.6 Exercises and Projects . 90 4.7 References. 92 . 5 Mathematical Models in Classical Cryptology 93 5.1 Introduction. 93 5.2 Some Terminology of
Cryptology. 94 5.3 Simple Substitution Systems within a General Crypto graphic Framework . 95 5.4 The Vigenére Cipher and One-Time Pads. 99 5.5 The Basic Hill System and Variations. 103 5.6 Exercises and Projects . 107 5.7 References. 112 6 Mathematical Models in Public-Key Cryptology 6.1 Introduction. 115 115
ix 6.2 Cryptosystems Based on Integer Factorization. 120 6.3 Cryptosystems Based on Discrete Logarithms. 126 6.4 Digital Signatures. 130 6.5 Exercises and Projects . 133 6.6 References. 135 7 Nonlinear Transverse Vibrations in an Elastic Medium 137 7.1 Introduction. 137 7.2 A String Embedded in an Elastic Medium . 138 7.3 An Approximation Technique for Nonlinear Differential Equations. 141 7.4 Base Equation Solution of Ricatti Equation. 143 7.5 Exercises and Projects . 145 7.6 References. 148 8 Simulating Networks with Time-Varying Arrivals 151 8.1 Introduction. 151 8.2 The Registration Problem . 152 8.3 Generating Random Numbers . 153 8.4 Statistical Tools. 160 8.5 Arrival Processes. 166 8.6 Queueing Models 172 8.7 Exercises and Projects
. 178 8.8 References. 182 . 9 Mathematical Modeling of Unsaturated Porous Media Flow and Transport 185 9.1 Introduction. . . 185 9.2 Governing Equations . 186 9.3 Constant-Coefficient Convection-Dispersion. 190 9.4 Coupling the Equations. 193 9.5 Summary and Suggestions for Further Study. 198 9.6 Exercises and Projects 200 .
x 9.7 References. 10 Inventory Replenishment Policies and Production Strategies 201 203 10.1 Introduction. 203 10.2 Piston Production and the Multinomial Model. 204 10.3 Sleeve Inventory Safety Stocks. 205 10.4 Comparison of Three Reordering Policies. 206 10.5 Variable Piston Production Quantities. 210 10.6 The Supplier’s Production Problem. 211 10.7 Target Selection for Multinomial Distributions. 220 10.8 The Supplier’s Cost Function. 222 10.9 Target Selection Using Normal Distributions. 223 10.10 Conclusion. 226 10.11 Exercises and Projects . 227 10.12 References. 229 11 Modeling Nonlinear Phenomena by Dynamical Systems 231 11.1 Introduction. 231 11.2 Simple Pendulum. 232 11.3 Periodically Forced Pendulum. 235 11.4 Exercises and Projects . 238 11.5
References. 240 12 Modulated Poisson Process Models for Bursty Traffic Behavior 241 12.1 Introduction. 241 12.2 Workstation Utilization Problem. 242 12.3 Constructing a Modulated Poisson Process. 244 12.4 Simulation Techniques. 255 12.5 Analysis Techniques. 260 12.6 Exercises and Projects . 264 12.7 References. 268
xi 13 Graph-Theoretic Analysis of FiniteMarkov Chains 271 13.1 Introduction. 271 13.2 State Classification . 272 13.3 Periodicity. 278 13.4 Conclusion. 286 13.5 Exercises and Projects . 286 13.6 References. 289 14 Some Error-Correcting Codes andTheirApplications 291 14.1 Introduction. 291 14.2 Background Coding Theory. 292 14.3 Computer Memories and Hamming Codes . 301 14.4 Photographs in Space and Reed-Muller Codes. 305 14.5 Compact Discs and Reed-SolomonCodes. 307 14.6 Conclusion. 311 14.7 Exercises and Projects . 311 14.8 References. 313 15 Broadcasting and Gossiping in Communication Networks 315 15.1 Introduction. 315 15.2 Standard Gossiping and Broadcasting. 316 15.3 Examples of
Communication. 321 15.4 Results from Selected Gossiping Problems . 327 15.5 Conclusion. 330 15.6 Exercises and Projects . 330 15.7 References. 331 16 Modeling the Impact of Environmental Regulations on Hydroelectric Revenues 333 16.1 Introduction. 333 16.2 Preliminaries. 334 16.3 Model Formulation 336 .
Xli 16.4 Model Development. 342 16.5 Case Study. 350 16.6 Exercises andProjects . 359 16.7 References. 362 17 Vertical Stabilization of a Rocket on a Movable Platform 363 17.1 Introduction. 363 17.2 Mathematical Model. 364 17.3 State-Space Control Theory . 367 17.4 The KNvD Algorithm. 370 17.5 Exercises and Projects . 372 17.6 References. 380 18 Distinguished Solutions of a Forced Oscillator 383 18.1 Introduction. 383 18.2 Linear Model with ModifiedExternal Forcing. 385 18.3 Nonlinear Oscillator PeriodicallyForced by Impulses . . 389 18.4 A Suspension Bridge Model. 394 18.5 Model Extension to Two SpatialDimensions. 398 18.6 Exercises and Projects . 399 18.7 References. 401 19 Mathematical Modeling and
Computer Simulation of a Polymerization Process 403 19.1 Introduction. 403 19.2 Formulating a Mathematical Model. 407 19.3 Computational Approach. 412 19.4 Conclusion. 418 19.5 Exercises and Projects . 420 19.6 References. 422
xiii A The Clemson Graduate Program in the Mathematical Sciences 423 A.l Introduction. 423 A.2 Historical Background. 424 A.3 Transformation of a Department. 426 A.4 The Clemson Program. 428 A.5 Communication Skills. 431 A.6 Program Governance. 432 A.7 Measures of Success . 433 A.8 Conclusion . 435 A.9 References. 435 Index 437 |
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| spelling | Shier, Douglas R. Verfasser aut Applied mathematical modeling a multidisciplinary approach D. R. Shier, K. T. Wallenius Boca Raton Chapman & Hall/CRC 2019 xxiv, 443 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Mathematical models Mathematisches Modell (DE-588)4114528-8 s DE-604 Wallenius, Kenneth T. Verfasser (DE-588)173398723 aut Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032441078&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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