Topics in mathematical modeling:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ [u.a.]
Princeton Univ. Press
2007
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [287] - 291 |
| Physical Description: | XV, 300 S. Ill., graph. Darst. |
| ISBN: | 9780691116426 0691116423 |
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| adam_text | TOPICS IN MATHEMATICAL MODELING K. K. TUNG PRINCETON UNIVERSITY PRESS
PRINCETON AND OXFORD CONTENTS PREFACE XIII FIBONACCI NUMBERS, THE GOLDEN
RATIO, AND LAWS OF NATURE? 1.1 LEONARDO FIBONACCI 1 1.2 THE GOLDEN RATIO
7 1.3 THE GOLDEN RECTANGLE AND SELF-SIMILARITY 10 1.4 PHYLLOTAXIS 12 1.5
PINECONES, SUNFLOWERS, AND OTHER SEED HEADS 15 1.6 THE HOFMEISTER RULE
17 1.7 A DYNAMICAL MODEL 20 1.8 CONCLUDING REMARKS 21 1.9 EXERCISES 22
SCALING LAWS OF LIFE, THE INTERNET, AND SOCIAL NETWORKS 2.1 INTRODUCTION
27 2.2 LAW OF QUARTER POWERS 27 2.3 A MODEL OF BRANCHING VASCULAR
NETWORKS 30 2.4 PREDICTIONS OF THE MODEL 35 2.5 COMPLICATIONS AND
MODIFICATIONS 36 2.6 THE FOURTH FRACTAL DIMENSION OF LIFE 38 2.7 ZIPF S
LAW OF HUMAN LANGUAGE, OF THE SIZE OF CITIES, AND EMAIL 39 2.8 THE WORLD
WIDE WEB AND THE ACTOR S NETWORK 42 2.9 MATHEMATICAL MODELING OF
CITATION NETWORK AND THE WEB 44 2.10 EXERCISES 47 MODELING CHANGE ONE
STEP AT A TIME 3.1 INTRODUCTION 54 3.2 COMPOUND INTEREST AND MORTGAGE
PAYMENTS 54 YOUR BANK ACCOUNT 54 YOUR MORTGAGE PAYMENTS, MONTHLY
INTEREST COMPOUNDING 56 YOUR MORTGAGE PAYMENTS, DAILY INTEREST
COMPOUNDING 57 3.3 SOME EXAMPLES 58 3.4 COMPOUNDING CONTINUOUSLY 58
CONTINUOUS COMPOUNDING 59 DOUBLE MY MONEY: RULE OF 72, OR IS IT RULE
OF 69 ? 60 VIII CONTENTS 3.5 RATE OF CHANGE 62 CONTINUOUS CHANGE 63 3.6
CHAOTIC BANK BALANCES 63 3.7 EXERCISES 65 DIFFERENTIAL EQUATION MODELS:
CARBON DATING, AGE OF THE UNIVERSE, HIV MODELING 4.1 INTRODUCTION 68 4.2
RADIOMETRIC DATING 68 4.3 THE AGE OF URANIUM IN OUR SOLAR SYSTEM 70 4.4
THE AGE OF THE UNIVERSE 71 4.5 CARBON DATING 74 4.6 HIV MODELING 77 4.7
EXERCISES 79 MODELING IN THE PHYSICAL SCIENCES, KEPLER, NEWTON, AND
CALCULUS 5.1 INTRODUCTION 84 5.2 CALCULUS, NEWTON, AND LEIBNIZ 87 5.3
VECTOR CALCULUS NEEDED 88 5.4 REWRITING KEPLER S LAWS MATHEMATICALLY 90
5.5 GENERALIZATIONS 93 5.6 NEWTON AND THE ELLIPTICAL ORBIT 95 5.7
EXERCISES 96 NONLINEAR POPULATION MODELS: AN INTRODUCTION TO QUALITATIVE
ANALYSIS USING PHASE PLANES 6.1 INTRODUCTION 98 6.2 POPULATION MODELS 98
6.3 QUALITATIVE ANALYSIS 100 6.4 HARVESTING MODELS 101 6.5 ECONOMIC
CONSIDERATIONS 103 6.6 DEPENSATION GROWTH MODELS 104 6.7 COMMENTS 108
6.8 EXERCISES 108 DISCRETE TIME LOGISTIC MAP, PERIODIC AND CHAOTIC
SOLUTIONS 7.1 INTRODUCTION 113 LOGISTIC GROWTH FOR NONOVERLAPPING
GENERATIONS 114 7.2 DISCRETE MAP 115 7.3 NONLINEAR SOLUTION 117 CONTENTS
IX 8 7.4 SENSITIVITY TO INITIAL CONDITIONS 7.5 ORDER OUT OF CHAOS 7.6
CHAOS IS NOT RANDOM 7.7 EXERCISES SNOWBALL EARTH AND GLOBAL WARMING 8.1
INTRODUCTION 8.2 SIMPLE CLIMATE MODELS INCOMING SOLAR RADIATION ALBEDO
OUTWARD RADIATION ICE DYNAMICS TRANSPORT THE MODEL EQUATION 8.3 THE
EQUILIBRIUM SOLUTIONS ICE-FREE GLOBE ICE-COVERED GLOBE PARTIALLY
ICE-COVERED GLOBE MULTIPLE EQUILIBRIA 8.4 STABILITY THE SLOPE-STABILITY
THEOREM THE STABILITY OF THE ICE-FREE AND ICE-COVERED GLOBES STABILITY
AND INSTABILITY OF THE PARTIALLY ICE-COVERED GLOBE HOW DOES A SNOWBALL
EARTH END? 8.5 EVIDENCE OF A SNOWBALL EARTH AND ITS FIERY END 8.6 THE
GLOBAL WARMING CONTROVERSY 8.7 A SIMPLE EQUATION FOR CLIMATE
PERTURBATION 8.8 SOLUTIONS EQUILIBRIUM GLOBAL WARMING TIME-DEPENDENT
GLOBAL WARMING THERMAL INERTIA OF THE ATMOSPHERE-OCEAN SYSTEM 8.9
EXERCISES 120 121 122 122 126 128 129 130 130 132 132 133 134 135 136
137 138 139 140 141 141 143 144 146 150 153 153 154 155 157
INTERACTIONS: PREDATOR-PREY, SPRAYING OF PESTS, CARNIVORES IN AUSTRALIA
9.1 INTRODUCTION 161 9.2 THE NONLINEAR SYSTEM AND ITS LINEAR STABILITY
162 9.3 LOTKA-VOLTERRA PREDATOR-PREY MODEL 165 LINEAR ANALYSIS 167
NONLINEAR ANALYSIS 170 9.4 HARVESTING OF PREDATOR AND PREY 172
INDISCRIMINATE SPRAYING OF INSECTS 173 CONTENTS 9.5 THE CASE OF THE
MISSING LARGE MAMMALIAN CARNIVORES 173 9.6 COMMENT 176 9.7 MORE EXAMPLES
OF INTERACTIONS 178 9.8 EXERCISES 182 MARRIAGE AND DIVORCE 10.1
INTRODUCTION 191 10.2 MATHEMATICAL MODELING 195 SELF-INTERACTION 196
MARITAL INTERACTIONS 197 10.3 DATA 198 10.4 AN EXAMPLE OF A VALIDATING
COUPLE 199 10.5 WHY AVOIDING CONFLICTS IS AN EFFECTIVE STRATEGY IN
MARRIAGE 201 10.6 TERMINOLOGY 202 10.7 GENERAL EQUILIBRIUM SOLUTIONS 203
10.8 CONCLUSION 206 10.9 ASSIGNMENT 206 10.10 EXERCISES 210 11 CHAOS IN
DETERMINISTIC CONTINUOUS SYSTEMS, POINCARE AND LORENZ 12 11.1 11.2 11.3
11.4 11.5 11.6 11.7 INTRODUCTION HENRI POINCARE EDWARD LORENZ THE LORENZ
EQUATIONS COMMENTS ON LORENZ EQUATIONS AS A MODEL OF CONVECTION CHAOTIC
WATERWHEEL EXERCISES EL NINO AND THE SOUTHERN OSCILLATION 12.1 12.2 12.3
12.4 12.5 12.6 INTRODUCTION BJERKNES HYPOTHESIS A SIMPLE MATHEMATICAL
MODEL OF EL NINO THE ATMOSPHERE AIR-SEA INTERACTION OCEAN TEMPERATURE
ADVECTION OTHER MODELS OF EL NINO APPENDIX: THE ADVECTION EQUATION
EXERCISES 212 212 214 216 224 225 226 229 231 233 233 234 235 239 240
241 CONTENTS XI AGE OF THE EARTH: LORD KELVIN S MODEL 13.1 INTRODUCTION
243 13.2 THE HEAT CONDUCTION PROBLEM 245 13.3 NUMBERS 250 13.4 EXERCISES
251 14 COLLAPSING BRIDGES: BROUGHTON AND TACOMA NARROWS 14.1
INTRODUCTION 254 14.2 MARCHING SOLDIERS ON A BRIDGE: A SIMPLE MODEL 254
RESONANCE 259 A DIFFERENT FORCING FUNCTION 260 14.3 TACOMA NARROWS
BRIDGE 261 ASSIGNMENT 262 14.4 EXERCISES 262 APPENDIX A: DIFFERENTIAL
EQUATIONS AND THEIR SOLUTIONS A.I FIRST-AND SECOND-ORDER EQUATIONS 267
A.2 NONHOMOGENEOUS ORDINARY DIFFERENTIAL EQUATIONS 273 FIRST-ORDER
EQUATIONS 273 SECOND-ORDER EQUATIONS 275 A.3 SUMMARY OF ODE SOLUTIONS
277 A.4 EXERCISES 278 A.5 SOLUTIONS TO EXERCISES 279 APPENDIX B: MATLAB
CODES B.I MATLAB CODES FOR LORENZ EQUATIONS 282 B.2 MATLAB CODES FOR
SOLVING VALLIS S EQUATIONS 284 BIBLIOGRAPHY 287 INDEX 293
|
| adam_txt |
TOPICS IN MATHEMATICAL MODELING K. K. TUNG PRINCETON UNIVERSITY PRESS
PRINCETON AND OXFORD CONTENTS PREFACE XIII FIBONACCI NUMBERS, THE GOLDEN
RATIO, AND LAWS OF NATURE? 1.1 LEONARDO FIBONACCI 1 1.2 THE GOLDEN RATIO
7 1.3 THE GOLDEN RECTANGLE AND SELF-SIMILARITY 10 1.4 PHYLLOTAXIS 12 1.5
PINECONES, SUNFLOWERS, AND OTHER SEED HEADS 15 1.6 THE HOFMEISTER RULE
17 1.7 A DYNAMICAL MODEL 20 1.8 CONCLUDING REMARKS 21 1.9 EXERCISES 22
SCALING LAWS OF LIFE, THE INTERNET, AND SOCIAL NETWORKS 2.1 INTRODUCTION
27 2.2 LAW OF QUARTER POWERS 27 2.3 A MODEL OF BRANCHING VASCULAR
NETWORKS 30 2.4 PREDICTIONS OF THE MODEL 35 2.5 COMPLICATIONS AND
MODIFICATIONS 36 2.6 THE FOURTH FRACTAL DIMENSION OF LIFE 38 2.7 ZIPF'S
LAW OF HUMAN LANGUAGE, OF THE SIZE OF CITIES, AND EMAIL 39 2.8 THE WORLD
WIDE WEB AND THE ACTOR'S NETWORK 42 2.9 MATHEMATICAL MODELING OF
CITATION NETWORK AND THE WEB 44 2.10 EXERCISES 47 MODELING CHANGE ONE
STEP AT A TIME 3.1 INTRODUCTION 54 3.2 COMPOUND INTEREST AND MORTGAGE
PAYMENTS 54 YOUR BANK ACCOUNT 54 YOUR MORTGAGE PAYMENTS, MONTHLY
INTEREST COMPOUNDING 56 YOUR MORTGAGE PAYMENTS, DAILY INTEREST
COMPOUNDING 57 3.3 SOME EXAMPLES 58 3.4 COMPOUNDING CONTINUOUSLY 58
CONTINUOUS COMPOUNDING 59 DOUBLE MY MONEY: "RULE OF 72," OR IS IT "RULE
OF 69"? 60 VIII CONTENTS 3.5 RATE OF CHANGE 62 CONTINUOUS CHANGE 63 3.6
CHAOTIC BANK BALANCES 63 3.7 EXERCISES 65 DIFFERENTIAL EQUATION MODELS:
CARBON DATING, AGE OF THE UNIVERSE, HIV MODELING 4.1 INTRODUCTION 68 4.2
RADIOMETRIC DATING 68 4.3 THE AGE OF URANIUM IN OUR SOLAR SYSTEM 70 4.4
THE AGE OF THE UNIVERSE 71 4.5 CARBON DATING 74 4.6 HIV MODELING 77 4.7
EXERCISES 79 MODELING IN THE PHYSICAL SCIENCES, KEPLER, NEWTON, AND
CALCULUS 5.1 INTRODUCTION 84 5.2 CALCULUS, NEWTON, AND LEIBNIZ 87 5.3
VECTOR CALCULUS NEEDED 88 5.4 REWRITING KEPLER'S LAWS MATHEMATICALLY 90
5.5 GENERALIZATIONS 93 5.6 NEWTON AND THE ELLIPTICAL ORBIT 95 5.7
EXERCISES 96 NONLINEAR POPULATION MODELS: AN INTRODUCTION TO QUALITATIVE
ANALYSIS USING PHASE PLANES 6.1 INTRODUCTION 98 6.2 POPULATION MODELS 98
6.3 QUALITATIVE ANALYSIS 100 6.4 HARVESTING MODELS 101 6.5 ECONOMIC
CONSIDERATIONS 103 6.6 DEPENSATION GROWTH MODELS 104 6.7 COMMENTS 108
6.8 EXERCISES 108 DISCRETE TIME LOGISTIC MAP, PERIODIC AND CHAOTIC
SOLUTIONS 7.1 INTRODUCTION 113 LOGISTIC GROWTH FOR NONOVERLAPPING
GENERATIONS 114 7.2 DISCRETE MAP 115 7.3 NONLINEAR SOLUTION 117 CONTENTS
IX 8 7.4 SENSITIVITY TO INITIAL CONDITIONS 7.5 ORDER OUT OF CHAOS 7.6
CHAOS IS NOT RANDOM 7.7 EXERCISES SNOWBALL EARTH AND GLOBAL WARMING 8.1
INTRODUCTION 8.2 SIMPLE CLIMATE MODELS INCOMING SOLAR RADIATION ALBEDO
OUTWARD RADIATION ICE DYNAMICS TRANSPORT THE MODEL EQUATION 8.3 THE
EQUILIBRIUM SOLUTIONS ICE-FREE GLOBE ICE-COVERED GLOBE PARTIALLY
ICE-COVERED GLOBE MULTIPLE EQUILIBRIA 8.4 STABILITY THE SLOPE-STABILITY
THEOREM THE STABILITY OF THE ICE-FREE AND ICE-COVERED GLOBES STABILITY
AND INSTABILITY OF THE PARTIALLY ICE-COVERED GLOBE HOW DOES A SNOWBALL
EARTH END? 8.5 EVIDENCE OF A SNOWBALL EARTH AND ITS FIERY END 8.6 THE
GLOBAL WARMING CONTROVERSY 8.7 A SIMPLE EQUATION FOR CLIMATE
PERTURBATION 8.8 SOLUTIONS EQUILIBRIUM GLOBAL WARMING TIME-DEPENDENT
GLOBAL WARMING THERMAL INERTIA OF THE ATMOSPHERE-OCEAN SYSTEM 8.9
EXERCISES 120 121 122 122 126 128 129 130 130 132 132 133 134 135 136
137 138 139 140 141 141 143 144 146 150 153 153 154 155 157
INTERACTIONS: PREDATOR-PREY, SPRAYING OF PESTS, CARNIVORES IN AUSTRALIA
9.1 INTRODUCTION 161 9.2 THE NONLINEAR SYSTEM AND ITS LINEAR STABILITY
162 9.3 LOTKA-VOLTERRA PREDATOR-PREY MODEL 165 LINEAR ANALYSIS 167
NONLINEAR ANALYSIS 170 9.4 HARVESTING OF PREDATOR AND PREY 172
INDISCRIMINATE SPRAYING OF INSECTS 173 CONTENTS 9.5 THE CASE OF THE
MISSING LARGE MAMMALIAN CARNIVORES 173 9.6 COMMENT 176 9.7 MORE EXAMPLES
OF INTERACTIONS 178 9.8 EXERCISES 182 MARRIAGE AND DIVORCE 10.1
INTRODUCTION 191 10.2 MATHEMATICAL MODELING 195 SELF-INTERACTION 196
MARITAL INTERACTIONS 197 10.3 DATA 198 10.4 AN EXAMPLE OF A VALIDATING
COUPLE 199 10.5 WHY AVOIDING CONFLICTS IS AN EFFECTIVE STRATEGY IN
MARRIAGE 201 10.6 TERMINOLOGY 202 10.7 GENERAL EQUILIBRIUM SOLUTIONS 203
10.8 CONCLUSION 206 10.9 ASSIGNMENT 206 10.10 EXERCISES 210 11 CHAOS IN
DETERMINISTIC CONTINUOUS SYSTEMS, POINCARE AND LORENZ 12 11.1 11.2 11.3
11.4 11.5 11.6 11.7 INTRODUCTION HENRI POINCARE EDWARD LORENZ THE LORENZ
EQUATIONS COMMENTS ON LORENZ EQUATIONS AS A MODEL OF CONVECTION CHAOTIC
WATERWHEEL EXERCISES EL NINO AND THE SOUTHERN OSCILLATION 12.1 12.2 12.3
12.4 12.5 12.6 INTRODUCTION BJERKNES' HYPOTHESIS A SIMPLE MATHEMATICAL
MODEL OF EL NINO THE ATMOSPHERE AIR-SEA INTERACTION OCEAN TEMPERATURE
ADVECTION OTHER MODELS OF EL NINO APPENDIX: THE ADVECTION EQUATION
EXERCISES 212 212 214 216 224 225 226 229 231 233 233 234 235 239 240
241 CONTENTS XI AGE OF THE EARTH: LORD KELVIN'S MODEL 13.1 INTRODUCTION
243 13.2 THE HEAT CONDUCTION PROBLEM 245 13.3 NUMBERS 250 13.4 EXERCISES
251 14 COLLAPSING BRIDGES: BROUGHTON AND TACOMA NARROWS 14.1
INTRODUCTION 254 14.2 MARCHING SOLDIERS ON A BRIDGE: A SIMPLE MODEL 254
RESONANCE 259 A DIFFERENT FORCING FUNCTION 260 14.3 TACOMA NARROWS
BRIDGE 261 ASSIGNMENT 262 14.4 EXERCISES 262 APPENDIX A: DIFFERENTIAL
EQUATIONS AND THEIR SOLUTIONS A.I FIRST-AND SECOND-ORDER EQUATIONS 267
A.2 NONHOMOGENEOUS ORDINARY DIFFERENTIAL EQUATIONS 273 FIRST-ORDER
EQUATIONS 273 SECOND-ORDER EQUATIONS 275 A.3 SUMMARY OF ODE SOLUTIONS
277 A.4 EXERCISES 278 A.5 SOLUTIONS TO EXERCISES 279 APPENDIX B: MATLAB
CODES B.I MATLAB CODES FOR LORENZ EQUATIONS 282 B.2 MATLAB CODES FOR
SOLVING VALLIS'S EQUATIONS 284 BIBLIOGRAPHY 287 INDEX 293 |
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| index_date | 2024-07-02T19:52:52Z |
| indexdate | 2024-07-09T21:11:36Z |
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| language | English |
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| spelling | Tung, Ka-Kit Verfasser aut Topics in mathematical modeling K. K. Tung Princeton, NJ [u.a.] Princeton Univ. Press 2007 XV, 300 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. [287] - 291 Modèles mathématiques Mathematisches Modell Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 s DE-604 http://www.gbv.de/dms/goettingen/527986607.pdf lizenzfrei Inhaltsverzeichnis GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016326851&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tung, Ka-Kit Topics in mathematical modeling Modèles mathématiques Mathematisches Modell Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4114528-8 |
| title | Topics in mathematical modeling |
| title_auth | Topics in mathematical modeling |
| title_exact_search | Topics in mathematical modeling |
| title_exact_search_txtP | Topics in mathematical modeling |
| title_full | Topics in mathematical modeling K. K. Tung |
| title_fullStr | Topics in mathematical modeling K. K. Tung |
| title_full_unstemmed | Topics in mathematical modeling K. K. Tung |
| title_short | Topics in mathematical modeling |
| title_sort | topics in mathematical modeling |
| topic | Modèles mathématiques Mathematisches Modell Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Modèles mathématiques Mathematisches Modell Mathematical models |
| url | http://www.gbv.de/dms/goettingen/527986607.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016326851&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT tungkakit topicsinmathematicalmodeling |
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