Topics in Mathematical Modeling

ISBN-10: 0691116423
ISBN-13: 9780691116426
Edition: 2007
Authors: K. K. Tung
List price: $95.00 Buy it from $16.74
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Description: 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,  More...

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Book details

List price: $95.00
Copyright year: 2007
Publisher: Princeton University Press
Publication date: 4/15/2007
Binding: Hardcover
Pages: 336
Size: 7.00" wide x 10.00" long x 1.00" tall
Weight: 1.848
Language: English

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 Nio. 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.

Preface
Fibonacci Numbers, the Golden Ratio, and Laws of Nature?
Leonardo Fibonacci
The Golden Ratio
The Golden Rectangle and Self-Similarity
Phyllotaxis
Pinecones, Sunflowers, and Other Seed Heads
The Hofmeister Rule
A DynamicalModel
Concluding Remarks
Exercises
Scaling Laws of Life, the Internet, and Social Networks
Introduction
Law of Quarter Powers
A Model of Branching Vascular Networks
Predictions of theModel
Complications andModifications
The Fourth Fractal Dimension of Life
Zipf's Law of Human Language, of the Size of Cities, and Email
TheWorldWideWeb and the Actor's Network
MathematicalModeling of Citation Network and theWeb
0 Exercises
Modeling Change One Step at a Time
Introduction
Compound Interest and Mortgage Payments 54
Your Bank Account
Your Mortgage Payments,Monthly Interest Compounding
Your Mortgage Payments, Daily Interest Compounding
Some Examples
Compounding Continuously
Continuous Compounding
Double My Money: "Rule of 72," or Is It "Rule of 69"?
Rate of Change
Continuous Change
Chaotic Bank Balances
Exercises
Differential Equation Models: Carbon Dating, Age of the Universe, HIV Modeling
Introduction
Radiometric Dating
The Age of Uranium in Our Solar System
The Age of the Universe
Carbon Dating
HIV Modeling
Exercises
Modeling in the Physical Sciences, Kepler, Newton, and Calculus
Introduction
Calculus, Newton, and Leibniz
Vector Calculus Needed
Rewriting Kepler's Laws Mathematically
Generalizations
Newton and the Elliptical Orbit
Exercises
Nonlinear Population Models: An Introduction to Qualitative Analysis Using Phase Planes
Introduction
PopulationModels
Qualitative Analysis
HarvestingModels
Economic Considerations
Depensation Growth Models
Comments
Exercises
Discrete Time Logistic Map, Periodic and Chaotic Solutions
Introduction
Logistic Growth for Nonoverlapping Generations
DiscreteMap
Nonlinear Solution
Sensitivity to Initial Conditions
Order Out of Chaos
Chaos Is Not Random
Exercises
Snowball Earth and Global Warming
Introduction
Simple ClimateModels
Incoming Solar Radiation
Albedo
Outward Radiation
Ice Dynamics
Transport
TheModel Equation
The Equilibrium Solutions
Ice-Free Globe
Ice-Covered Globe
Partially Ice-Covered Globe
Multiple Equilibria
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?
Evidence of a Snowball Earth and Its Fiery End
The GlobalWarming Controversy
A Simple Equation for Climate Perturbation
Solutions
Equilibrium GlobalWarming
Time-Dependent GlobalWarming
Thermal Inertia of the Atmosphere-Ocean System
Exercises
Interactions: Predator-Prey, Spraying of Pests, Carnivores in Australia
Introduction
The Nonlinear System and Its Linear Stability
Lotka-Volterra Predator-Prey Model
Linear Analysis
Nonlinear Analysis
Harvesting of Predator and Prey
Indiscriminate Spraying of Insects
The Case of theMissing Large Mammalian

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