Topics in Mathematical Modeling

Ka-Kit Tung

• Publisher: Princeton University Press
• Year: 2016
• Print ISBN:
  9780691116426
• eBook ISBN:
  9781400884056
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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 Niño. 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.

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Dedication Page
• Contents
• Preface
• Chapter 1: Fibonacci Numbers, the Golden Ratio, and Laws of Nature?
• Chapter 2: Scaling Laws of Life, the Internet, and Social Networks
• Chapter 3: Modeling Change One Step at a Time
• Chapter 4: Differential Equation Models: Carbon Dating, Age of the Universe, HIV Modeling
• Chapter 5: Modeling in the Physical Sciences, Kepler, Newton, and Calculus
• Chapter 6: Nonlinear Population Models: An Introduction to Qualitative Analysis Using Phase Planes
• Chapter 7: Discrete Time Logistic Map, Periodic and Chaotic Solutions
• Chapter 8: Snowball Earth and Global Warming
• Chapter 9: Interactions: Predator–Prey, Spraying of Pests, Carnivores in Australia
• Chapter 10: Marriage and Divorce
• Chapter 11: Chaos in Deterministic Continuous Systems, Poincaré and Lorenz
• Chapter 12: El Niño and the Southern Oscillation
• Chapter 13: Age of the Earth: Lord Kelvin's Model
• Chapter 14: Collapsing Bridges: Broughton and Tacoma Narrows
• APPENDIX A: Differential Equations and Their Solutions
• APPENDIX B: MATLAB Codes
• Bibliography
• Index