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Topics in Mathematical Modeling - K. K. Tung

Topics in Mathematical Modeling

Hardcover Published: 26th March 2007
ISBN: 9780691116426
Number Of Pages: 336

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"Topics in Mathematical Modeling" is an introductory textbook on mathematical modeling. The book teaches how simple mathematics can help formulate and solve real problems of current research interest in a wide range of fields, including biology, ecology, computer science, geophysics, engineering, and the social sciences. Yet the prerequisites are minimal: calculus and elementary differential equations. Among the many topics addressed are HIV; plant phyllotaxis; global warming; the World Wide Web; plant and animal vascular networks; social networks; chaos and fractals; marriage and divorce; and El Nino. Traditional modeling topics such as predator-prey interaction, harvesting, and wars of attrition are also included. Most chapters begin with the history of a problem, follow with a demonstration of how it can be modeled using various mathematical tools, and close with a discussion of its remaining unsolved aspects.

Designed for a one-semester course, the book progresses from problems that can be solved with relatively simple mathematics to ones that require more sophisticated methods. The math techniques are taught as needed to solve the problem being addressed, and each chapter is designed to be largely independent to give teachers flexibility.

The book, which can be used as an overview and introduction to applied mathematics, is particularly suitable for sophomore, junior, and senior students in math, science, and engineering.

"This beautifully produced book should provide a joyful and stimulating reading experience for any layman who is curious about real-life events in the context of mathematical modelling, and it provides an excellent entry point to more advanced areas such as mathematical biology or climate modelling."--Z. Q. John Lu, Significance "What do global warming, predator-prey interactions, and the World Wide Web have in common? All of these disparate phenomena can be modeled using mathematics. In Topics in Mathematical Modeling, K. K. Tung demonstrates math?s relevance to problems of current research interest in biology, ecology, computer science, geophysics, engineering, and the social sciences."--Scientific American Book Club "[T]his is a good introductory book about the nature and purpose of mathematical modeling. The topics chosen and the way in which they have been motivated and presented will help a wide range of students to 'see the point' and thereby arouse and stimulate their confidence about their mathematical problem solving skills."--Bob Anderssen, Australian Mathematics Society "I was so impressed by the breadth of examples contained in its 336 pages that I immediately set about using it to update one of my own undergraduate courses... A wonderful source book for all kinds of undergraduate mathematical activities... Extremely clear... It is highly recommended."--Chris Howls, Times Higher Education "Tung's preface shows that he is a dyed-in-the-wool teacher of considerable talent whose only mission is to show the student how to take raw empirical data and turn it into a mathematical paradigm that can be analyzed. His prerequisites are solid but minimal: calculus and a smattering of ordinary differential equations (ODEs). He is wise to provide an appendix with a quick treatment of ODEs for those whose background is deficient. Tung also describes in the preface a clear path for those who wish to avoid the differential equations altogether. Tung covers some of the usual modeling topics but also many others that are surprising and refreshing."--Steven G. Krantz, UMAP Journal

Prefacep. xiii
Fibonacci Numbers, the Golden Ratio, and Laws of Nature?
Leonardo Fibonaccip. 1
The Golden Ratiop. 7
The Golden Rectangle and Self-Similarityp. 10
Phyllotaxisp. 12
Pinecones, Sunflowers, and Other Seed Headsp. 15
The Hofmeister Rulep. 17
A DynamicalModelp. 20
Concluding Remarksp. 21
Exercisesp. 22
Scaling Laws of Life, the Internet, and Social Networks
Introductionp. 27
Law of Quarter Powersp. 27
A Model of Branching Vascular Networksp. 30
Predictions of theModelp. 35
Complications andModificationsp. 36
The Fourth Fractal Dimension of Lifep. 38
Zipf's Law of Human Language, of the Size of Cities, and Emailp. 39
TheWorldWideWeb and the Actor's Networkp. 42
MathematicalModeling of Citation Network and theWebp. 44
0 Exercisesp. 47
Modeling Change One Step at a Time
Introductionp. 54
Compound Interest and Mortgage Payments 54
Your Bank Accountp. 54
Your Mortgage Payments,Monthly Interest Compoundingp. 56
Your Mortgage Payments, Daily Interest Compoundingp. 57
Some Examplesp. 58
Compounding Continuouslyp. 58
Continuous Compoundingp. 59
Double My Money: "Rule of 72," or Is It "Rule of 69"?p. 60
Rate of Changep. 62
Continuous Changep. 63
Chaotic Bank Balancesp. 63
Exercisesp. 65
Differential Equation Models: Carbon Dating, Age of the Universe, HIV Modeling
Introductionp. 68
Radiometric Datingp. 68
The Age of Uranium in Our Solar Systemp. 70
The Age of the Universep. 71
Carbon Datingp. 74
HIV Modelingp. 77
Exercisesp. 79
Modeling in the Physical Sciences, Kepler, Newton, and Calculus
Introductionp. 84
Calculus, Newton, and Leibnizp. 87
Vector Calculus Neededp. 88
Rewriting Kepler's Laws Mathematicallyp. 90
Generalizationsp. 93
Newton and the Elliptical Orbitp. 95
Exercisesp. 96
Nonlinear Population Models: An Introduction to Qualitative Analysis Using Phase Planes
Introductionp. 98
PopulationModelsp. 98
Qualitative Analysisp. 100
HarvestingModelsp. 101
Economic Considerationsp. 103
Depensation Growth Modelsp. 104
Commentsp. 108
Exercisesp. 108
Discrete Time Logistic Map, Periodic and Chaotic Solutions
Introductionp. 113
Logistic Growth for Nonoverlapping Generationsp. 114
DiscreteMapp. 115
Nonlinear Solutionp. 117
Sensitivity to Initial Conditionsp. 120
Order Out of Chaosp. 121
Chaos Is Not Randomp. 122
Exercisesp. 122
Snowball Earth and Global Warming
Introductionp. 126
Simple ClimateModelsp. 128
Incoming Solar Radiationp. 129
Albedop. 130
Outward Radiationp. 130
Ice Dynamicsp. 132
Transportp. 132
TheModel Equationp. 133
The Equilibrium Solutionsp. 134
Ice-Free Globep. 135
Ice-Covered Globep. 136
Partially Ice-Covered Globep. 137
Multiple Equilibriap. 138
Stabilityp. 139
The Slope-Stability Theoremp. 140
The Stability of the Ice-Free and Ice-Covered Globesp. 141
Stability and Instability of the Partially Ice-Covered Globep. 141
How Does a Snowball Earth End?p. 143
Evidence of a Snowball Earth and Its Fiery Endp. 144
The GlobalWarming Controversyp. 146
A Simple Equation for Climate Perturbationp. 150
Solutionsp. 153
Equilibrium GlobalWarmingp. 153
Time-Dependent GlobalWarmingp. 154
Thermal Inertia of the Atmosphere-Ocean Systemp. 155
Exercisesp. 157
Interactions: Predator-Prey, Spraying of Pests, Carnivores in Australia
Introductionp. 161
The Nonlinear System and Its Linear Stabilityp. 162
Lotka-Volterra Predator-Prey Modelp. 165
Linear Analysisp. 167
Nonlinear Analysisp. 170
Harvesting of Predator and Preyp. 172
Indiscriminate Spraying of Insectsp. 173
The Case of theMissing Large Mammalian
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780691116426
ISBN-10: 0691116423
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 336
Published: 26th March 2007
Publisher: Princeton University Press
Country of Publication: US
Dimensions (cm): 25.4 x 18.03  x 2.29
Weight (kg): 0.68

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